[{"OA_type":"hybrid","citation":{"mla":"Kwan, Matthew Alan, et al. “Counting Perfect Matchings in Dirac Hypergraphs.” <i>Combinatorica</i>, vol. 46, 5, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00493-025-00194-8\">10.1007/s00493-025-00194-8</a>.","chicago":"Kwan, Matthew Alan, Roodabeh Safavi Hemami, and Yiting Wang. “Counting Perfect Matchings in Dirac Hypergraphs.” <i>Combinatorica</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00493-025-00194-8\">https://doi.org/10.1007/s00493-025-00194-8</a>.","ieee":"M. A. Kwan, R. Safavi Hemami, and Y. Wang, “Counting perfect matchings in Dirac hypergraphs,” <i>Combinatorica</i>, vol. 46. Springer Nature, 2026.","ista":"Kwan MA, Safavi Hemami R, Wang Y. 2026. Counting perfect matchings in Dirac hypergraphs. Combinatorica. 46, 5.","apa":"Kwan, M. A., Safavi Hemami, R., &#38; Wang, Y. (2026). Counting perfect matchings in Dirac hypergraphs. <i>Combinatorica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00493-025-00194-8\">https://doi.org/10.1007/s00493-025-00194-8</a>","ama":"Kwan MA, Safavi Hemami R, Wang Y. Counting perfect matchings in Dirac hypergraphs. <i>Combinatorica</i>. 2026;46. doi:<a href=\"https://doi.org/10.1007/s00493-025-00194-8\">10.1007/s00493-025-00194-8</a>","short":"M.A. Kwan, R. Safavi Hemami, Y. Wang, Combinatorica 46 (2026)."},"article_number":"5","corr_author":"1","has_accepted_license":"1","OA_place":"publisher","oa_version":"Published Version","language":[{"iso":"eng"}],"volume":46,"month":"02","department":[{"_id":"MaKw"},{"_id":"MoHe"}],"author":[{"last_name":"Kwan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan"},{"last_name":"Safavi Hemami","full_name":"Safavi Hemami, Roodabeh","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154","first_name":"Roodabeh"},{"id":"1917d194-076e-11ed-97cd-837255f88785","first_name":"Yiting","orcid":"0000-0002-2856-767X","full_name":"Wang, Yiting","last_name":"Wang"}],"publication_status":"published","acknowledgement":"We would like to thank the referees for a number of helpful comments and suggestions, which have substantially improved the paper. Open access funding provided by Institute of Science and Technology (IST Austria).","scopus_import":"1","ddc":["510"],"intvolume":"        46","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"file":[{"date_updated":"2026-02-16T09:52:38Z","checksum":"47b0031d90b0e6b9a843f422a1486089","content_type":"application/pdf","file_id":"21228","success":1,"access_level":"open_access","file_size":539646,"creator":"dernst","relation":"main_file","date_created":"2026-02-16T09:52:38Z","file_name":"2026_Combinatorica_Kwan.pdf"}],"quality_controlled":"1","abstract":[{"text":"One of the foundational theorems of extremal graph theory is Dirac’s theorem, which\r\nsays that if an n-vertex graph G has minimum degree at least n/2, then G has a\r\nHamilton cycle, and therefore a perfect matching (if n is even). Later work by Sárközy,\r\nSelkow and Szemerédi showed that in fact Dirac graphs have many Hamilton cycles\r\nand perfect matchings, culminating in a result of Cuckler and Kahn that gives a precise\r\ndescription of the numbers of Hamilton cycles and perfect matchings in a Dirac graph\r\nG (in terms of an entropy-like parameter of G). In this paper we extend Cuckler\r\nand Kahn’s result to perfect matchings in hypergraphs. For positive integers d < k,\r\nand for n divisible by k, let md (k, n) be the minimum d-degree that ensures the\r\nexistence of a perfect matching in an n-vertex k-uniform hypergraph. In general, it is\r\nan open question to determine (even asymptotically) the values of md (k, n), but we are\r\nnonetheless able to prove an analogue of the Cuckler–Kahn theorem, showing that if\r\nan n-vertex k-uniform hypergraph G has minimum d-degree at least (1+γ )md (k, n)\r\n(for any constantγ > 0), then the number of perfect matchings in G is controlled by\r\nan entropy-like parameter of G. This strengthens cruder estimates arising from work\r\nof Kang–Kelly–Kühn–Osthus–Pfenninger and Pham–Sah–Sawhney–Simkin.","lang":"eng"}],"title":"Counting perfect matchings in Dirac hypergraphs","PlanS_conform":"1","publisher":"Springer Nature","oa":1,"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"doi":"10.1007/s00493-025-00194-8","date_updated":"2026-02-16T09:55:17Z","status":"public","arxiv":1,"file_date_updated":"2026-02-16T09:52:38Z","year":"2026","external_id":{"arxiv":["2408.09589"]},"_id":"21159","date_published":"2026-02-01T00:00:00Z","date_created":"2026-02-08T23:02:49Z","publication":"Combinatorica","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","day":"01","article_processing_charge":"Yes (via OA deal)"},{"OA_place":"publisher","ec_funded":1,"has_accepted_license":"1","issue":"2","OA_type":"gold","article_number":"P2.24","corr_author":"1","citation":{"apa":"Morawski, P., &#38; Petrova, K. H. (2026). Randomly perturbed digraphs also have bounded-degree spanning trees. <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href=\"https://doi.org/10.37236/13316\">https://doi.org/10.37236/13316</a>","ama":"Morawski P, Petrova KH. Randomly perturbed digraphs also have bounded-degree spanning trees. <i>Electronic Journal of Combinatorics</i>. 2026;33(2). doi:<a href=\"https://doi.org/10.37236/13316\">10.37236/13316</a>","short":"P. Morawski, K.H. Petrova, Electronic Journal of Combinatorics 33 (2026).","mla":"Morawski, Patryk, and Kalina H. Petrova. “Randomly Perturbed Digraphs Also Have Bounded-Degree Spanning Trees.” <i>Electronic Journal of Combinatorics</i>, vol. 33, no. 2, P2.24, Electronic Journal of Combinatorics, 2026, doi:<a href=\"https://doi.org/10.37236/13316\">10.37236/13316</a>.","chicago":"Morawski, Patryk, and Kalina H Petrova. “Randomly Perturbed Digraphs Also Have Bounded-Degree Spanning Trees.” <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2026. <a href=\"https://doi.org/10.37236/13316\">https://doi.org/10.37236/13316</a>.","ieee":"P. Morawski and K. H. Petrova, “Randomly perturbed digraphs also have bounded-degree spanning trees,” <i>Electronic Journal of Combinatorics</i>, vol. 33, no. 2. Electronic Journal of Combinatorics, 2026.","ista":"Morawski P, Petrova KH. 2026. Randomly perturbed digraphs also have bounded-degree spanning trees. Electronic Journal of Combinatorics. 33(2), P2.24."},"acknowledgement":"We thank the anonymous referees for many helpful comments on an earlier version of this\r\narticle. Kalina Petrova was supported by grant no. CRSII5 173721 of the Swiss National\r\nScience Foundation, and by the European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie Sk lodowska-Curie grant agreement No. 101034413","ddc":["510"],"intvolume":"        33","scopus_import":"1","month":"05","volume":33,"publication_status":"published","author":[{"first_name":"Patryk","full_name":"Morawski, Patryk","last_name":"Morawski"},{"first_name":"Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","full_name":"Petrova, Kalina H","last_name":"Petrova"}],"department":[{"_id":"MaKw"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"DOAJ_listed":"1","project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"status":"public","date_updated":"2026-05-18T08:50:18Z","doi":"10.37236/13316","arxiv":1,"oa":1,"article_type":"original","tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"file":[{"date_created":"2026-05-18T08:46:26Z","relation":"main_file","file_size":399969,"creator":"dernst","access_level":"open_access","file_name":"2026_ElectrJournCombinatorics_Morawski.pdf","date_updated":"2026-05-18T08:46:26Z","success":1,"file_id":"21893","checksum":"9e8402cb2e8870ba7ded9ae7b308201a","content_type":"application/pdf"}],"publisher":"Electronic Journal of Combinatorics","title":"Randomly perturbed digraphs also have bounded-degree spanning trees","abstract":[{"text":"We show that a randomly perturbed digraph, where we start with a dense digraph Dα and add a small number of random edges to it, will typically contain a fixed orientation of a bounded-degree spanning tree. This answers a question posed by Araujo, Balogh, Krueger, Piga and Treglown and generalizes the corresponding result for randomly perturbed graphs by Krivelevich, Kwan and Sudakov. More specifically, we prove that there exists a constant c=c(α,Δ) such that if \r\nT is an oriented tree with maximum degree Δ and Dα is an n-vertex digraph with minimum semidegree αn, then the graph obtained by adding cn uniformly random edges to Dα will contain T with high probability.","lang":"eng"}],"quality_controlled":"1","publication_identifier":{"eissn":["1077-8926"]},"article_processing_charge":"Yes","day":"08","publication":"Electronic Journal of Combinatorics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","date_published":"2026-05-08T00:00:00Z","external_id":{"arxiv":["2306.14648"]},"_id":"21884","date_created":"2026-05-17T22:02:11Z","file_date_updated":"2026-05-18T08:46:26Z","year":"2026"},{"file_date_updated":"2026-01-05T13:29:34Z","year":"2026","date_published":"2026-01-01T00:00:00Z","external_id":{"arxiv":["2402.01447"],"isi":["001585783400001"]},"_id":"20422","date_created":"2025-10-05T22:01:34Z","publication":"Journal of Combinatorial Theory Series B","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","day":"01","publication_identifier":{"eissn":["1096-0902"],"issn":["0095-8956"]},"file":[{"date_updated":"2026-01-05T13:29:34Z","success":1,"content_type":"application/pdf","file_id":"20953","checksum":"60676af4af4b3243ba187e7d65440d99","date_created":"2026-01-05T13:29:34Z","relation":"main_file","creator":"dernst","file_size":688924,"access_level":"open_access","file_name":"2026_JourCombTheoryB_Christoph.pdf"}],"publisher":"Elsevier","quality_controlled":"1","abstract":[{"text":"We show that if n is odd and p>=Clog n/n, then with high probability Hamilton cycles in G(n,p) span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph G, that is, a graph G with odd n vertices and minimum degree n/2+C for sufficiently large constant C, span its cycle space.\r\n","lang":"eng"}],"PlanS_conform":"1","title":"The Hamilton space of pseudorandom graphs","oa":1,"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"status":"public","date_updated":"2026-01-05T13:29:52Z","doi":"10.1016/j.jctb.2025.09.002","arxiv":1,"page":"254-267","oa_version":"Published Version","language":[{"iso":"eng"}],"volume":176,"month":"01","isi":1,"publication_status":"published","author":[{"first_name":"Micha","full_name":"Christoph, Micha","last_name":"Christoph"},{"full_name":"Nenadov, Rajko","last_name":"Nenadov","first_name":"Rajko"},{"last_name":"Petrova","full_name":"Petrova, Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","first_name":"Kalina H"}],"department":[{"_id":"MaKw"}],"acknowledgement":"This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. Image 1 Part of this research was conducted while the author was at Department of Computer Science, ETH Zürich, Switzerland. This author was supported by grant no. CRSII5 173721 of the Swiss National Science Foundation.","intvolume":"       176","ddc":["510"],"scopus_import":"1","OA_type":"hybrid","corr_author":"1","citation":{"ama":"Christoph M, Nenadov R, Petrova KH. The Hamilton space of pseudorandom graphs. <i>Journal of Combinatorial Theory Series B</i>. 2026;176:254-267. doi:<a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">10.1016/j.jctb.2025.09.002</a>","apa":"Christoph, M., Nenadov, R., &#38; Petrova, K. H. (2026). The Hamilton space of pseudorandom graphs. <i>Journal of Combinatorial Theory Series B</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">https://doi.org/10.1016/j.jctb.2025.09.002</a>","short":"M. Christoph, R. Nenadov, K.H. Petrova, Journal of Combinatorial Theory Series B 176 (2026) 254–267.","chicago":"Christoph, Micha, Rajko Nenadov, and Kalina H Petrova. “The Hamilton Space of Pseudorandom Graphs.” <i>Journal of Combinatorial Theory Series B</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">https://doi.org/10.1016/j.jctb.2025.09.002</a>.","ieee":"M. Christoph, R. Nenadov, and K. H. Petrova, “The Hamilton space of pseudorandom graphs,” <i>Journal of Combinatorial Theory Series B</i>, vol. 176. Elsevier, pp. 254–267, 2026.","mla":"Christoph, Micha, et al. “The Hamilton Space of Pseudorandom Graphs.” <i>Journal of Combinatorial Theory Series B</i>, vol. 176, Elsevier, 2026, pp. 254–67, doi:<a href=\"https://doi.org/10.1016/j.jctb.2025.09.002\">10.1016/j.jctb.2025.09.002</a>.","ista":"Christoph M, Nenadov R, Petrova KH. 2026. The Hamilton space of pseudorandom graphs. Journal of Combinatorial Theory Series B. 176, 254–267."},"ec_funded":1,"has_accepted_license":"1","OA_place":"publisher"},{"publication_identifier":{"issn":["0195-6698"]},"publisher":"Elsevier","title":"Odd-Ramsey numbers of complete bipartite graphs","PlanS_conform":"1","quality_controlled":"1","abstract":[{"text":"In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs H in Kn, defined as the minimum number of colours needed to colour the edges of K so that every copy of a graph H E H intersects some colour class in an odd number of edges. In this paper, we focus on complete bipartite graphs. First, we completely resolve the problem when H is the family of all spanning complete bipartite graphs on n vertices. We then focus on its subfamilies, that is, {Kt,n-t : t E T} for a fixed set of integers T c [[n/2]]. We prove that the odd-Ramsey problem is equivalent to determining the maximum dimension of a linear binary code avoiding codewords of given weights, and leverage known results from coding theory to deduce asymptotically tight bounds in our setting. We conclude with bounds for the odd-Ramsey numbers of fixed (that is, non-spanning) complete bipartite subgraphs.","lang":"eng"}],"file":[{"file_size":563029,"access_level":"open_access","creator":"dernst","relation":"main_file","date_created":"2026-01-05T13:34:40Z","file_name":"2026_EuropJourCombinatorics_Boyadzhiyska.pdf","date_updated":"2026-01-05T13:34:40Z","content_type":"application/pdf","checksum":"52883daa217398396cbf9b8ad9ddae92","file_id":"20954","success":1}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","oa":1,"arxiv":1,"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"status":"public","doi":"10.1016/j.ejc.2025.104235","date_updated":"2026-01-05T13:34:48Z","year":"2026","file_date_updated":"2026-01-05T13:34:40Z","date_created":"2025-10-16T13:14:34Z","date_published":"2026-01-01T00:00:00Z","_id":"20482","external_id":{"isi":["001573380700001"],"arxiv":["2410.05887"]},"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"European Journal of Combinatorics","article_processing_charge":"Yes (via OA deal)","day":"01","article_number":"104235","corr_author":"1","citation":{"ista":"Boyadzhiyska S, Das S, Lesgourgues T, Petrova KH. 2026. Odd-Ramsey numbers of complete bipartite graphs. European Journal of Combinatorics. 131, 104235.","chicago":"Boyadzhiyska, Simona, Shagnik Das, Thomas Lesgourgues, and Kalina H Petrova. “Odd-Ramsey Numbers of Complete Bipartite Graphs.” <i>European Journal of Combinatorics</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">https://doi.org/10.1016/j.ejc.2025.104235</a>.","ieee":"S. Boyadzhiyska, S. Das, T. Lesgourgues, and K. H. Petrova, “Odd-Ramsey numbers of complete bipartite graphs,” <i>European Journal of Combinatorics</i>, vol. 131. Elsevier, 2026.","mla":"Boyadzhiyska, Simona, et al. “Odd-Ramsey Numbers of Complete Bipartite Graphs.” <i>European Journal of Combinatorics</i>, vol. 131, 104235, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">10.1016/j.ejc.2025.104235</a>.","short":"S. Boyadzhiyska, S. Das, T. Lesgourgues, K.H. Petrova, European Journal of Combinatorics 131 (2026).","ama":"Boyadzhiyska S, Das S, Lesgourgues T, Petrova KH. Odd-Ramsey numbers of complete bipartite graphs. <i>European Journal of Combinatorics</i>. 2026;131. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">10.1016/j.ejc.2025.104235</a>","apa":"Boyadzhiyska, S., Das, S., Lesgourgues, T., &#38; Petrova, K. H. (2026). Odd-Ramsey numbers of complete bipartite graphs. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">https://doi.org/10.1016/j.ejc.2025.104235</a>"},"OA_type":"hybrid","has_accepted_license":"1","ec_funded":1,"OA_place":"publisher","language":[{"iso":"eng"}],"oa_version":"Published Version","isi":1,"publication_status":"published","author":[{"last_name":"Boyadzhiyska","full_name":"Boyadzhiyska, Simona","first_name":"Simona"},{"first_name":"Shagnik","full_name":"Das, Shagnik","last_name":"Das"},{"first_name":"Thomas","full_name":"Lesgourgues, Thomas","last_name":"Lesgourgues"},{"id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","first_name":"Kalina H","last_name":"Petrova","full_name":"Petrova, Kalina H"}],"department":[{"_id":"MaKw"}],"month":"01","volume":131,"ddc":["500"],"intvolume":"       131","scopus_import":"1","acknowledgement":"The authors would like to thank Gilles Zémor for a helpful clarification on [3], Deepak Bal and Patrick Bennett for bringing [25] to their attention, and both referees for several helpful comments.\r\nS.B.: Most of this research was conducted while the author was at the School of Mathematics, University of Birmingham, Birmingham, United Kingdom. The research leading to these results was supported by EPSRC, United Kingdom, grant no. EP/V048287/1 and by ERC Advanced Grants “GeoScape”, no. 882971 and “ERMiD”, no. 101054936. There are no additional data beyond that contained within the main manuscript.\r\nS.D.: Research supported by Taiwan NSTC grants 111-2115-M-002-009-MY2 and 113-2628-M-002-008-MY4.\r\nK.P.: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. Parts of this research was conducted while K.P. was at the Department of Computer Science, ETH Zürich, Switzerland, supported by Swiss National Science Foundation, Switzerland , grant no. CRSII5 173721."},{"issue":"12","OA_type":"hybrid","article_number":"rnag126","corr_author":"1","citation":{"short":"Z. Hunter, M.A. Kwan, L. Sauermann, M. Sawhney, International Mathematics Research Notices 2026 (2026).","apa":"Hunter, Z., Kwan, M. A., Sauermann, L., &#38; Sawhney, M. (2026). On random matrices with large corank. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnag126\">https://doi.org/10.1093/imrn/rnag126</a>","ama":"Hunter Z, Kwan MA, Sauermann L, Sawhney M. On random matrices with large corank. <i>International Mathematics Research Notices</i>. 2026;2026(12). doi:<a href=\"https://doi.org/10.1093/imrn/rnag126\">10.1093/imrn/rnag126</a>","ista":"Hunter Z, Kwan MA, Sauermann L, Sawhney M. 2026. On random matrices with large corank. International Mathematics Research Notices. 2026(12), rnag126.","mla":"Hunter, Zach, et al. “On Random Matrices with Large Corank.” <i>International Mathematics Research Notices</i>, vol. 2026, no. 12, rnag126, Oxford University Press, 2026, doi:<a href=\"https://doi.org/10.1093/imrn/rnag126\">10.1093/imrn/rnag126</a>.","chicago":"Hunter, Zach, Matthew Alan Kwan, Lisa Sauermann, and Mehtaab Sawhney. “On Random Matrices with Large Corank.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2026. <a href=\"https://doi.org/10.1093/imrn/rnag126\">https://doi.org/10.1093/imrn/rnag126</a>.","ieee":"Z. Hunter, M. A. Kwan, L. Sauermann, and M. Sawhney, “On random matrices with large corank,” <i>International Mathematics Research Notices</i>, vol. 2026, no. 12. Oxford University Press, 2026."},"has_accepted_license":"1","OA_place":"publisher","das_tickbox":"0","supplementarymaterial":"no","oa_version":"Published Version","language":[{"iso":"eng"}],"volume":2026,"month":"06","publication_status":"published","author":[{"full_name":"Hunter, Zach","last_name":"Hunter","first_name":"Zach"},{"first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"},{"first_name":"Lisa","last_name":"Sauermann","full_name":"Sauermann, Lisa"},{"first_name":"Mehtaab","full_name":"Sawhney, Mehtaab","last_name":"Sawhney"}],"department":[{"_id":"MaKw"}],"acknowledgement":"Z.H. was supported by SNSF grant 200021-228014. M.K. was supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. L.S. was supported by the Deutsche Forschungsgemeinschaft (DFG, German\r\nResearch Foundation)—CRC 1720–539309657. This research was conducted during the period M.S. served\r\nas a Clay Research Fellow. This work began when the authors were visiting Mathematisches Forschungsinstitut Oberwolfach, which\r\nprovided ideal working conditions. M.S. thanks Vishesh Jain for initial discussions regarding the problem.\r\nWe also thank the anonymous referee for helpful comments.","intvolume":"      2026","ddc":["500"],"scopus_import":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"file":[{"date_updated":"2026-06-29T09:15:15Z","content_type":"application/pdf","file_id":"22151","checksum":"396b47d0532d7ea509f8cd30f11392a8","success":1,"file_size":524993,"creator":"dernst","access_level":"open_access","relation":"main_file","date_created":"2026-06-29T09:15:15Z","file_name":"2026_IMRN_Hunter.pdf"}],"researchdata_availability":"no","publisher":"Oxford University Press","title":"On random matrices with large corank","PlanS_conform":"1","abstract":[{"text":"Let 1 ≤ k ≤ n and M be a random n × n matrix with independent uniformly random {±1}-entries. We\r\nshow that there exists an absolute constant c > 0 such that\r\nP[rank(M) ≤ n − k] ≤ exp(−cnk).\r\nThis confirms a well-known prediction in the area, extending a result of Rudelson (who previously\r\nproved this same result under the restriction k ≤ √n, via different methods).","lang":"eng"}],"quality_controlled":"1","oa":1,"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"doi":"10.1093/imrn/rnag126","status":"public","date_updated":"2026-06-29T09:19:14Z","arxiv":1,"file_date_updated":"2026-06-29T09:15:15Z","year":"2026","date_published":"2026-06-01T00:00:00Z","_id":"22147","external_id":{"arxiv":["2510.12933"]},"date_created":"2026-06-28T22:01:35Z","publication":"International Mathematics Research Notices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","article_processing_charge":"Yes (via OA deal)","day":"01"},{"day":"01","article_processing_charge":"No","publication":"arXiv","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"21211","external_id":{"arxiv":["2508.00480"]},"date_published":"2025-08-01T00:00:00Z","date_created":"2026-02-10T11:32:41Z","year":"2025","doi":"10.48550/arXiv.2508.00480","date_updated":"2026-02-10T11:39:16Z","status":"public","project":[{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"arxiv":1,"oa":1,"abstract":[{"lang":"eng","text":"We show that, for any graph F and η > 0, there exists a d0 = d0(F, η) such that every nvertex d-regular graph with d ≥ d0 has a collection of vertex-disjoint F-subdivisions covering\r\nat least (1 − η)n vertices. This verifies a conjecture of Verstraëte from 2002 and improves a\r\nrecent result of Letzter, Methuku and Sudakov which additionally required d to be at least\r\npolylogarithmic in n.\r\n"}],"title":"Packing subdivisions into regular graphs","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2508.00480"}],"acknowledgement":"Supported by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (grant agreement No. 947978). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.","month":"08","department":[{"_id":"MaKw"}],"author":[{"first_name":"Richard","full_name":"Montgomery, Richard","last_name":"Montgomery"},{"id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","first_name":"Kalina H","last_name":"Petrova","full_name":"Petrova, Kalina H"},{"first_name":"Arjun","last_name":"Ranganathan","full_name":"Ranganathan, Arjun"},{"first_name":"Jane","full_name":"Tan, Jane","last_name":"Tan"}],"publication_status":"submitted","oa_version":"Preprint","language":[{"iso":"eng"}],"OA_place":"repository","ec_funded":1,"OA_type":"green","citation":{"short":"R. Montgomery, K.H. Petrova, A. Ranganathan, J. Tan, ArXiv (n.d.).","ama":"Montgomery R, Petrova KH, Ranganathan A, Tan J. Packing subdivisions into regular graphs. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2508.00480\">10.48550/arXiv.2508.00480</a>","apa":"Montgomery, R., Petrova, K. H., Ranganathan, A., &#38; Tan, J. (n.d.). Packing subdivisions into regular graphs. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2508.00480\">https://doi.org/10.48550/arXiv.2508.00480</a>","ista":"Montgomery R, Petrova KH, Ranganathan A, Tan J. Packing subdivisions into regular graphs. arXiv, 2508.00480.","chicago":"Montgomery, Richard, Kalina H Petrova, Arjun Ranganathan, and Jane Tan. “Packing Subdivisions into Regular Graphs.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2508.00480\">https://doi.org/10.48550/arXiv.2508.00480</a>.","ieee":"R. Montgomery, K. H. Petrova, A. Ranganathan, and J. Tan, “Packing subdivisions into regular graphs,” <i>arXiv</i>. .","mla":"Montgomery, Richard, et al. “Packing Subdivisions into Regular Graphs.” <i>ArXiv</i>, 2508.00480, doi:<a href=\"https://doi.org/10.48550/arXiv.2508.00480\">10.48550/arXiv.2508.00480</a>."},"article_number":"2508.00480"},{"publication_identifier":{"issn":["0010-437X"],"eissn":["1570-5846"]},"publisher":"Cambridge University Press","abstract":[{"lang":"eng","text":"Consider a quadratic polynomial Q(ξ1, . . . , ξn) of independent Rademacher random variables ξ1, . . . , ξn. To what extent can Q(ξ1, . . . , ξn) concentrate on a single value? This quadratic version of the classical Littlewood–Offord problem was popularised by Costello, Tao and Vu in their study of symmetric random matrices. In this paper, we obtain an essentially optimal bound for this problem, as conjectured by Nguyen and Vu. Specifically, if Q(ξ1, . . . , ξn) ‘robustly depends on at least m of the ξi’ in the sense that there is no way to pin down the value of Q(ξ1, . . . , ξn) by fixing values for fewer than m of the variables ξi, then we have Pr[Q(ξ1, . . . , ξn) = 0] ≤ O(1/√m). This also implies a similar result in the case where ξ1, . . . , ξn have arbitrary distributions. Our proof combines a number of ideas that may be of independent interest, including an inductive decoupling scheme that reduces quadratic anticoncentration problems\r\nto high-dimensional linear anticoncentration problems. Also, one application of our main result is the resolution of a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn related to graph inducibility. "}],"quality_controlled":"1","title":"Resolution of the quadratic Littlewood–Offord problem","PlanS_conform":"1","file":[{"date_updated":"2026-05-04T09:41:25Z","success":1,"file_id":"21787","content_type":"application/pdf","checksum":"bd3415bb435da9d0b39f6f9a18c61abb","date_created":"2026-05-04T09:41:25Z","relation":"main_file","access_level":"open_access","creator":"dernst","file_size":858727,"file_name":"2025_CompositioMath_Kwan.pdf"}],"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"arxiv":1,"project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics","grant_number":"101076777"}],"doi":"10.1112/S0010437X25102789","date_updated":"2026-05-04T09:42:57Z","status":"public","year":"2025","file_date_updated":"2026-05-04T09:41:25Z","date_created":"2026-04-12T22:01:48Z","date_published":"2025-12-01T00:00:00Z","external_id":{"arxiv":["2312.13826"]},"_id":"21706","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Compositio Mathematica","article_processing_charge":"Yes (via OA deal)","day":"01","corr_author":"1","citation":{"apa":"Kwan, M. A., &#38; Sauermann, L. (2025). Resolution of the quadratic Littlewood–Offord problem. <i>Compositio Mathematica</i>. Cambridge University Press. <a href=\"https://doi.org/10.1112/S0010437X25102789\">https://doi.org/10.1112/S0010437X25102789</a>","ama":"Kwan MA, Sauermann L. Resolution of the quadratic Littlewood–Offord problem. <i>Compositio Mathematica</i>. 2025;161(12):3089-3139. doi:<a href=\"https://doi.org/10.1112/S0010437X25102789\">10.1112/S0010437X25102789</a>","short":"M.A. Kwan, L. Sauermann, Compositio Mathematica 161 (2025) 3089–3139.","mla":"Kwan, Matthew Alan, and Lisa Sauermann. “Resolution of the Quadratic Littlewood–Offord Problem.” <i>Compositio Mathematica</i>, vol. 161, no. 12, Cambridge University Press, 2025, pp. 3089–139, doi:<a href=\"https://doi.org/10.1112/S0010437X25102789\">10.1112/S0010437X25102789</a>.","ieee":"M. A. Kwan and L. Sauermann, “Resolution of the quadratic Littlewood–Offord problem,” <i>Compositio Mathematica</i>, vol. 161, no. 12. Cambridge University Press, pp. 3089–3139, 2025.","chicago":"Kwan, Matthew Alan, and Lisa Sauermann. “Resolution of the Quadratic Littlewood–Offord Problem.” <i>Compositio Mathematica</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1112/S0010437X25102789\">https://doi.org/10.1112/S0010437X25102789</a>.","ista":"Kwan MA, Sauermann L. 2025. Resolution of the quadratic Littlewood–Offord problem. Compositio Mathematica. 161(12), 3089–3139."},"issue":"12","OA_type":"hybrid","has_accepted_license":"1","OA_place":"publisher","language":[{"iso":"eng"}],"page":"3089-3139","oa_version":"Published Version","publication_status":"published","department":[{"_id":"MaKw"}],"author":[{"first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","last_name":"Kwan","full_name":"Kwan, Matthew Alan"},{"first_name":"Lisa","last_name":"Sauermann","full_name":"Sauermann, Lisa"}],"volume":161,"month":"12","intvolume":"       161","ddc":["510"],"scopus_import":"1","acknowledgement":"We would like to thank the anonymous referee for a number of helpful comments and suggestions. Matthew Kwan was supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. Lisa Sauermann was supported in part by NSF Award DMS-2100157 and a Sloan Research Fellowship, and in part by the DFG Heisenberg Program."},{"citation":{"chicago":"Anastos, Michael, Simona Boyadzhiyska, Silas Rathke, and Juanjo Rué. “On the Chromatic Number of Powers of Subdivisions of Graphs.” <i>Discrete Applied Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">https://doi.org/10.1016/j.dam.2024.10.002</a>.","ieee":"M. Anastos, S. Boyadzhiyska, S. Rathke, and J. Rué, “On the chromatic number of powers of subdivisions of graphs,” <i>Discrete Applied Mathematics</i>, vol. 360. Elsevier, pp. 506–511, 2025.","mla":"Anastos, Michael, et al. “On the Chromatic Number of Powers of Subdivisions of Graphs.” <i>Discrete Applied Mathematics</i>, vol. 360, Elsevier, 2025, pp. 506–11, doi:<a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">10.1016/j.dam.2024.10.002</a>.","ista":"Anastos M, Boyadzhiyska S, Rathke S, Rué J. 2025. On the chromatic number of powers of subdivisions of graphs. Discrete Applied Mathematics. 360, 506–511.","ama":"Anastos M, Boyadzhiyska S, Rathke S, Rué J. On the chromatic number of powers of subdivisions of graphs. <i>Discrete Applied Mathematics</i>. 2025;360:506-511. doi:<a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">10.1016/j.dam.2024.10.002</a>","apa":"Anastos, M., Boyadzhiyska, S., Rathke, S., &#38; Rué, J. (2025). On the chromatic number of powers of subdivisions of graphs. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.dam.2024.10.002\">https://doi.org/10.1016/j.dam.2024.10.002</a>","short":"M. Anastos, S. Boyadzhiyska, S. Rathke, J. Rué, Discrete Applied Mathematics 360 (2025) 506–511."},"corr_author":"1","OA_type":"hybrid","has_accepted_license":"1","ec_funded":1,"OA_place":"publisher","language":[{"iso":"eng"}],"oa_version":"Published Version","page":"506-511","department":[{"_id":"MaKw"}],"author":[{"full_name":"Anastos, Michael","last_name":"Anastos","first_name":"Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb"},{"last_name":"Boyadzhiyska","full_name":"Boyadzhiyska, Simona","first_name":"Simona"},{"full_name":"Rathke, Silas","last_name":"Rathke","first_name":"Silas"},{"first_name":"Juanjo","full_name":"Rué, Juanjo","last_name":"Rué"}],"isi":1,"publication_status":"published","volume":360,"month":"01","scopus_import":"1","ddc":["510"],"intvolume":"       360","acknowledgement":"This work was initiated at the annual workshop of the Combinatorics and Graph Theory group of Freie Universität Berlin in Wilhelmsaue in September 2023. The authors would like to thank the institution for enabling this research. Finally, the fourth author would like to thank Tibor Szabó and the Combinatorics and Graph Theory group at Freie Universität Berlin for their hospitality during the research visit. Additionally, we thank Moharram Iradmusa for bringing the papers [5], [7] to our attention. Finally, we thank the anonymous referees for their suggestions on the manuscript, which have improved the quality of the document.\r\nM.A.: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413 .\r\nS.B.: The research leading to these results was supported by EPSRC, UK, grant no. EP/V048287/1. There are no additional data beyond that contained within the main manuscript.\r\nS.R.: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689).\r\nJ.R. acknowledges the support of the Grant PID2020-113082GB-I00 funded by MICIU/AEI/10.13039/501100011033, Spain, and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D, Spain (CEX2020-001084-M).","publication_identifier":{"issn":["0166-218X"]},"quality_controlled":"1","abstract":[{"lang":"eng","text":"For a given graph G=(V,E), we define its \\emph{nth subdivision} as the graph obtained from G by replacing every edge by a path of length n. We also define the \\emph{mth power} of G as the graph on vertex set V where we connect every pair of vertices at distance at most m in G. In this paper, we study the chromatic number of powers of subdivisions of graphs and resolve the case m=n asymptotically. In particular, our result confirms a conjecture of Mozafari-Nia and Iradmusa in the case m=n=3 in a strong sense."}],"title":"On the chromatic number of powers of subdivisions of graphs","publisher":"Elsevier","file":[{"date_updated":"2025-01-13T09:25:59Z","success":1,"file_id":"18836","content_type":"application/pdf","checksum":"bd20a13e56b3ea01daf5e7aca5247c60","relation":"main_file","date_created":"2025-01-13T09:25:59Z","file_size":441060,"access_level":"open_access","creator":"dernst","file_name":"2025_DiscreteApplMath_Anastos.pdf"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","oa":1,"arxiv":1,"date_updated":"2025-04-14T07:54:56Z","doi":"10.1016/j.dam.2024.10.002","status":"public","project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"year":"2025","file_date_updated":"2025-01-13T09:25:59Z","date_created":"2024-10-27T23:01:44Z","_id":"18478","external_id":{"arxiv":["2404.05542"],"isi":["001343647000001"]},"date_published":"2025-01-15T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","publication":"Discrete Applied Mathematics","day":"15","article_processing_charge":"Yes (in subscription journal)"},{"intvolume":"       125","ddc":["510"],"scopus_import":"1","acknowledgement":"We thank the anonymous referees for their careful proofreading which helped improve the presentation of this paper. We also thank one of the anonymous referees for pointing out our construction implies Theorem 1.7!\r\nBenjamin Moore finished this project while a postdoctoral researcher at Charles University, and was supported by project 22-17398S (Flows and cycles in graphs on surfaces) of the Czech Science Foundation. Benjamin Moore is currently funded by RANDSTRUCT No. 101076777, and appreciates the gracious support. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2020-03912]. Cette recherche a été financée par le Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG), [numéro de référence RGPIN-2020-03912]. This project was funded in part by the Government of Ontario .","publication_status":"published","isi":1,"department":[{"_id":"MaKw"}],"author":[{"full_name":"Carbonero, Alvaro","last_name":"Carbonero","first_name":"Alvaro"},{"last_name":"Koerts","full_name":"Koerts, Hidde","first_name":"Hidde"},{"first_name":"Benjamin","id":"6dc1a1be-bf1c-11ed-8d2b-d044840f49d6","full_name":"Moore, Benjamin","last_name":"Moore"},{"last_name":"Spirkl","full_name":"Spirkl, Sophie","first_name":"Sophie"}],"month":"03","volume":125,"language":[{"iso":"eng"}],"oa_version":"Published Version","OA_place":"publisher","has_accepted_license":"1","corr_author":"1","article_number":"104104","citation":{"ista":"Carbonero A, Koerts H, Moore B, Spirkl S. 2025. On heroes in digraphs with forbidden induced forests. European Journal of Combinatorics. 125, 104104.","ieee":"A. Carbonero, H. Koerts, B. Moore, and S. Spirkl, “On heroes in digraphs with forbidden induced forests,” <i>European Journal of Combinatorics</i>, vol. 125. Elsevier, 2025.","chicago":"Carbonero, Alvaro, Hidde Koerts, Benjamin Moore, and Sophie Spirkl. “On Heroes in Digraphs with Forbidden Induced Forests.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">https://doi.org/10.1016/j.ejc.2024.104104</a>.","mla":"Carbonero, Alvaro, et al. “On Heroes in Digraphs with Forbidden Induced Forests.” <i>European Journal of Combinatorics</i>, vol. 125, 104104, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">10.1016/j.ejc.2024.104104</a>.","short":"A. Carbonero, H. Koerts, B. Moore, S. Spirkl, European Journal of Combinatorics 125 (2025).","ama":"Carbonero A, Koerts H, Moore B, Spirkl S. On heroes in digraphs with forbidden induced forests. <i>European Journal of Combinatorics</i>. 2025;125. doi:<a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">10.1016/j.ejc.2024.104104</a>","apa":"Carbonero, A., Koerts, H., Moore, B., &#38; Spirkl, S. (2025). On heroes in digraphs with forbidden induced forests. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2024.104104\">https://doi.org/10.1016/j.ejc.2024.104104</a>"},"OA_type":"hybrid","article_processing_charge":"Yes (in subscription journal)","day":"01","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"European Journal of Combinatorics","date_created":"2025-01-05T23:01:55Z","date_published":"2025-03-01T00:00:00Z","_id":"18753","external_id":{"arxiv":["2306.04710"],"isi":["001400113700001"]},"year":"2025","file_date_updated":"2025-04-16T09:16:25Z","arxiv":1,"project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"doi":"10.1016/j.ejc.2024.104104","date_updated":"2025-05-19T14:06:00Z","status":"public","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publisher":"Elsevier","quality_controlled":"1","abstract":[{"text":"We continue a line of research which studies which hereditary families of digraphs have bounded dichromatic number. For a class of digraphs  C, a hero in  C  is any digraph  H\r\n  such that  H -free digraphs in  C  have bounded dichromatic number. We show that if  F\r\n  is an oriented star of degree at least five, the only heroes for the class of  F -free digraphs are transitive tournaments. For oriented stars  F  of degree exactly four, we show the only heroes in  F -free digraphs are transitive tournaments, or possibly special joins of transitive tournaments. Aboulker et al. characterized the set of heroes of  {H,K1+P2→} -free digraphs almost completely, and we show the same characterization for the class of  {H,rK1+P3→} -free digraphs. Lastly, we show that if we forbid two \"valid\" orientations of brooms, then every transitive tournament is a hero for this class of digraphs.","lang":"eng"}],"title":"On heroes in digraphs with forbidden induced forests","file":[{"date_created":"2025-04-16T09:16:25Z","relation":"main_file","access_level":"open_access","creator":"dernst","file_size":1110657,"file_name":"2025_EuropJournCombinatorics_Carbonero.pdf","date_updated":"2025-04-16T09:16:25Z","success":1,"checksum":"2c75f78f40ebb93d16fe3765bda2905a","content_type":"application/pdf","file_id":"19577"}],"publication_identifier":{"issn":["0195-6698"]}},{"publisher":"Elsevier","abstract":[{"lang":"eng","text":"A k-subcolouring of a graph G is a function f : V (G) → {0,...,k − 1} such that the set of\r\nvertices coloured i induce a disjoint union of cliques. The subchromatic number, χsub(G),\r\nis the minimum k such that G admits a k-subcolouring. Nešetril, ˇ Ossona de Mendez,\r\nPilipczuk, and Zhu (2020), recently raised the problem of finding tight upper bounds for\r\nχsub(G2) when G is planar. We show that χsub(G2) ≤ 43 when G is planar, improving\r\ntheir bound of 135. We give even better bounds when the planar graph G has larger girth.\r\nMoreover, we show that χsub(G3) ≤ 95, improving the previous bound of 364. For these\r\nwe adapt some recent techniques of Almulhim and Kierstead (2022), while also extending\r\nthe decompositions of triangulated planar graphs of Van den Heuvel, Ossona de Mendez,\r\nQuiroz, Rabinovich and Siebertz (2017), to planar graphs of arbitrary girth. Note that these\r\ndecompositions are the precursors of the graph product structure theorem of planar graphs.\r\nWe give improved bounds for χsub(Gp) for all p ≥ 2, whenever G has bounded treewidth,\r\nbounded simple treewidth, bounded genus, or excludes a clique or biclique as a minor.\r\nFor this we introduce a family of parameters which form a gradation between the strong\r\nand the weak colouring numbers. We give upper bounds for these parameters for graphs\r\ncoming from such classes.\r\nFinally, we give a 2-approximation algorithm for the subchromatic number of graphs\r\nhaving a layering in which each layer has bounded cliquewidth and this layering is\r\ncomputable in polynomial time (like the class of all dth powers of planar graphs, for fixed\r\nd). This algorithm works even if the power p and the graph G is unknown."}],"title":"Subchromatic numbers of powers of graphs with excluded minors","quality_controlled":"1","file":[{"date_updated":"2025-05-05T12:56:12Z","content_type":"application/pdf","checksum":"6723cbb02b6aea0d05f37d167da00c03","file_id":"19657","success":1,"file_size":850988,"creator":"dernst","access_level":"open_access","date_created":"2025-05-05T12:56:12Z","relation":"main_file","file_name":"2025_DiscreteMath_Cortes.pdf"}],"publication_identifier":{"issn":["0012-365X"]},"arxiv":1,"status":"public","doi":"10.1016/j.disc.2024.114377","date_updated":"2025-09-30T10:25:15Z","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","oa":1,"date_created":"2025-02-05T06:51:08Z","date_published":"2025-04-01T00:00:00Z","_id":"19002","external_id":{"arxiv":["2306.02195"],"isi":["001401656900001"]},"year":"2025","file_date_updated":"2025-05-05T12:56:12Z","article_processing_charge":"Yes (via OA deal)","day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","publication":"Discrete Mathematics","has_accepted_license":"1","corr_author":"1","article_number":"114377","citation":{"short":"P.P. Cortés, P. Kumar, B. Moore, P. Ossona de Mendez, D.A. Quiroz, Discrete Mathematics 348 (2025).","apa":"Cortés, P. P., Kumar, P., Moore, B., Ossona de Mendez, P., &#38; Quiroz, D. A. (2025). Subchromatic numbers of powers of graphs with excluded minors. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.disc.2024.114377\">https://doi.org/10.1016/j.disc.2024.114377</a>","ama":"Cortés PP, Kumar P, Moore B, Ossona de Mendez P, Quiroz DA. Subchromatic numbers of powers of graphs with excluded minors. <i>Discrete Mathematics</i>. 2025;348(4). doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114377\">10.1016/j.disc.2024.114377</a>","ista":"Cortés PP, Kumar P, Moore B, Ossona de Mendez P, Quiroz DA. 2025. Subchromatic numbers of powers of graphs with excluded minors. Discrete Mathematics. 348(4), 114377.","mla":"Cortés, Pedro P., et al. “Subchromatic Numbers of Powers of Graphs with Excluded Minors.” <i>Discrete Mathematics</i>, vol. 348, no. 4, 114377, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114377\">10.1016/j.disc.2024.114377</a>.","ieee":"P. P. Cortés, P. Kumar, B. Moore, P. Ossona de Mendez, and D. A. Quiroz, “Subchromatic numbers of powers of graphs with excluded minors,” <i>Discrete Mathematics</i>, vol. 348, no. 4. Elsevier, 2025.","chicago":"Cortés, Pedro P., Pankaj Kumar, Benjamin Moore, Patrice Ossona de Mendez, and Daniel A. Quiroz. “Subchromatic Numbers of Powers of Graphs with Excluded Minors.” <i>Discrete Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.disc.2024.114377\">https://doi.org/10.1016/j.disc.2024.114377</a>."},"OA_type":"hybrid","issue":"4","OA_place":"publisher","language":[{"iso":"eng"}],"oa_version":"Published Version","ddc":["510"],"intvolume":"       348","scopus_import":"1","acknowledgement":"We thank an anonymous referee for pointing out an error in an earlier version of Theorem 3.1. We also thank an anonymous referee for pointing out numerous typos in an earlier version of the paper.","isi":1,"publication_status":"published","author":[{"first_name":"Pedro P.","last_name":"Cortés","full_name":"Cortés, Pedro P."},{"last_name":"Kumar","full_name":"Kumar, Pankaj","first_name":"Pankaj"},{"last_name":"Moore","full_name":"Moore, Benjamin","id":"6dc1a1be-bf1c-11ed-8d2b-d044840f49d6","first_name":"Benjamin"},{"last_name":"Ossona de Mendez","full_name":"Ossona de Mendez, Patrice","first_name":"Patrice"},{"full_name":"Quiroz, Daniel A.","last_name":"Quiroz","first_name":"Daniel A."}],"department":[{"_id":"MaKw"}],"month":"04","volume":348},{"publisher":"Cambridge University Press","title":"On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7","abstract":[{"text":"Let f(r)(n;s,k) denote the maximum number of edges in an n-vertex r-uniform hypergraph containing no subgraph with k edges and at most s vertices. Brown, Erdős and Sós [New directions in the theory of graphs (Proc. Third Ann Arbor Conf., Univ. Michigan 1971), pp. 53--63, Academic Press 1973] conjectured that the limit limn→∞n−2f(3)(n;k+2,k) exists for all k. The value of the limit was previously determined for k=2 in the original paper of Brown, Erdős and Sós, for k=3 by Glock [Bull. Lond. Math. Soc. 51 (2019) 230--236] and for k=4 by Glock, Joos, Kim, Kühn, Lichev and Pikhurko [arXiv:2209.14177, accepted by Proc. Amer. Math. Soc.] while Delcourt and Postle [arXiv:2210.01105, accepted by Proc. Amer. Math. Soc.] proved the conjecture (without determining the limiting value).\r\nIn this paper, we determine the value of the limit in the Brown-Erdős-Sós Problem for k∈{5,6,7}. More generally, we obtain the value of limn→∞n−2f(r)(n;rk−2k+2,k) for all r≥3 and k∈{5,6,7}. In addition, by combining these new values with recent results of Bennett, Cushman and Dudek [arXiv:2309.00182] we obtain new asymptotic values for several generalised Ramsey numbers.","lang":"eng"}],"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.4153/s0008414x25000021","open_access":"1"}],"publication_identifier":{"issn":["0008-414X"],"eissn":["1496-4279"]},"status":"public","doi":"10.4153/s0008414x25000021","date_updated":"2025-09-30T10:28:07Z","arxiv":1,"oa":1,"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2025-01-06T00:00:00Z","external_id":{"arxiv":["2403.04474"],"isi":["001416788600001"]},"_id":"19017","date_created":"2025-02-10T08:39:46Z","year":"2025","article_processing_charge":"No","day":"06","publication":"Canadian Journal of Mathematics","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","has_accepted_license":"1","OA_type":"hybrid","citation":{"short":"S. Glock, J. Kim, L. Lichev, O. Pikhurko, S. Sun, Canadian Journal of Mathematics (2025) 1–43.","apa":"Glock, S., Kim, J., Lichev, L., Pikhurko, O., &#38; Sun, S. (2025). On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7. <i>Canadian Journal of Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.4153/s0008414x25000021\">https://doi.org/10.4153/s0008414x25000021</a>","ama":"Glock S, Kim J, Lichev L, Pikhurko O, Sun S. On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7. <i>Canadian Journal of Mathematics</i>. 2025:1-43. doi:<a href=\"https://doi.org/10.4153/s0008414x25000021\">10.4153/s0008414x25000021</a>","ista":"Glock S, Kim J, Lichev L, Pikhurko O, Sun S. 2025. On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7. Canadian Journal of Mathematics., 1–43.","mla":"Glock, Stefan, et al. “On the (k + 2, k)-Problem of Brown, Erdős, and Sós for k = 5,6,7.” <i>Canadian Journal of Mathematics</i>, Cambridge University Press, 2025, pp. 1–43, doi:<a href=\"https://doi.org/10.4153/s0008414x25000021\">10.4153/s0008414x25000021</a>.","ieee":"S. Glock, J. Kim, L. Lichev, O. Pikhurko, and S. Sun, “On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7,” <i>Canadian Journal of Mathematics</i>. Cambridge University Press, pp. 1–43, 2025.","chicago":"Glock, Stefan, Jaehoon Kim, Lyuben Lichev, Oleg Pikhurko, and Shumin Sun. “On the (k + 2, k)-Problem of Brown, Erdős, and Sós for k = 5,6,7.” <i>Canadian Journal of Mathematics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.4153/s0008414x25000021\">https://doi.org/10.4153/s0008414x25000021</a>."},"OA_place":"publisher","page":"1-43","oa_version":"Published Version","language":[{"iso":"eng"}],"ddc":["500"],"scopus_import":"1","month":"01","publication_status":"epub_ahead","isi":1,"department":[{"_id":"MaKw"}],"author":[{"full_name":"Glock, Stefan","last_name":"Glock","first_name":"Stefan"},{"last_name":"Kim","full_name":"Kim, Jaehoon","first_name":"Jaehoon"},{"full_name":"Lichev, Lyuben","last_name":"Lichev","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben"},{"first_name":"Oleg","full_name":"Pikhurko, Oleg","last_name":"Pikhurko"},{"first_name":"Shumin","last_name":"Sun","full_name":"Sun, Shumin"}]},{"date_updated":"2025-09-30T10:28:42Z","status":"public","doi":"10.1016/j.ejc.2025.104120","arxiv":1,"oa":1,"article_type":"original","publisher":"Elsevier","quality_controlled":"1","title":"The semi-random tree process","abstract":[{"text":"The online semi-random graph process is a one-player game which starts with the empty graph on n vertices. At every round, a player (called Builder) is presented with a vertex v chosen uniformly at random and independently from previous rounds, and constructs an edge of their choice that is incident to v. Inspired by recent advances on the semi-random graph process, we define a family of generalized online semi-random models.\r\nWe analyse a particular instance that shares similar features with the original semi-random graph process and determine the hitting times of the classical graph properties minimum degree k,k-connectivity, containment of a perfect matching, a Hamiltonian cycle and an \r\nH-factor for a fixed graph H possessing an additional tree-like property. Along the way, we derive a few consequences of the famous Aldous-Broder algorithm that may be of independent interest.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2204.07376","open_access":"1"}],"publication_identifier":{"issn":["0195-6698"]},"article_processing_charge":"No","day":"01","publication":"European Journal of Combinatorics","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","date_published":"2025-05-01T00:00:00Z","external_id":{"isi":["001420659400001"],"arxiv":["2204.07376 "]},"_id":"19018","date_created":"2025-02-10T09:00:53Z","year":"2025","OA_place":"repository","OA_type":"green","article_number":"104120","citation":{"chicago":"Burova, Sofiya, and Lyuben Lichev. “The Semi-Random Tree Process.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">https://doi.org/10.1016/j.ejc.2025.104120</a>.","ieee":"S. Burova and L. Lichev, “The semi-random tree process,” <i>European Journal of Combinatorics</i>, vol. 126. Elsevier, 2025.","mla":"Burova, Sofiya, and Lyuben Lichev. “The Semi-Random Tree Process.” <i>European Journal of Combinatorics</i>, vol. 126, 104120, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">10.1016/j.ejc.2025.104120</a>.","ista":"Burova S, Lichev L. 2025. The semi-random tree process. European Journal of Combinatorics. 126, 104120.","ama":"Burova S, Lichev L. The semi-random tree process. <i>European Journal of Combinatorics</i>. 2025;126. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">10.1016/j.ejc.2025.104120</a>","apa":"Burova, S., &#38; Lichev, L. (2025). The semi-random tree process. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104120\">https://doi.org/10.1016/j.ejc.2025.104120</a>","short":"S. Burova, L. Lichev, European Journal of Combinatorics 126 (2025)."},"acknowledgement":"We are grateful to Dieter Mitsche for related discussions and to several anonymous referees for multiple useful comments.","intvolume":"       126","scopus_import":"1","volume":126,"month":"05","publication_status":"published","isi":1,"author":[{"full_name":"Burova, Sofiya","last_name":"Burova","first_name":"Sofiya"},{"first_name":"Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","last_name":"Lichev","full_name":"Lichev, Lyuben"}],"department":[{"_id":"MaKw"}],"oa_version":"Preprint","language":[{"iso":"eng"}]},{"issue":"3","OA_type":"hybrid","article_number":"e70116","citation":{"ista":"Draganić N, Petrova KH. 2025. Size‐Ramsey numbers of graphs with maximum degree three. Journal of the London Mathematical Society. 111(3), e70116.","chicago":"Draganić, Nemanja, and Kalina H Petrova. “Size‐Ramsey Numbers of Graphs with Maximum Degree Three.” <i>Journal of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/jlms.70116\">https://doi.org/10.1112/jlms.70116</a>.","ieee":"N. Draganić and K. H. Petrova, “Size‐Ramsey numbers of graphs with maximum degree three,” <i>Journal of the London Mathematical Society</i>, vol. 111, no. 3. Wiley, 2025.","mla":"Draganić, Nemanja, and Kalina H. Petrova. “Size‐Ramsey Numbers of Graphs with Maximum Degree Three.” <i>Journal of the London Mathematical Society</i>, vol. 111, no. 3, e70116, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/jlms.70116\">10.1112/jlms.70116</a>.","short":"N. Draganić, K.H. Petrova, Journal of the London Mathematical Society 111 (2025).","ama":"Draganić N, Petrova KH. Size‐Ramsey numbers of graphs with maximum degree three. <i>Journal of the London Mathematical Society</i>. 2025;111(3). doi:<a href=\"https://doi.org/10.1112/jlms.70116\">10.1112/jlms.70116</a>","apa":"Draganić, N., &#38; Petrova, K. H. (2025). Size‐Ramsey numbers of graphs with maximum degree three. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.70116\">https://doi.org/10.1112/jlms.70116</a>"},"ec_funded":1,"has_accepted_license":"1","OA_place":"publisher","oa_version":"Published Version","language":[{"iso":"eng"}],"month":"03","volume":111,"publication_status":"published","isi":1,"department":[{"_id":"MaKw"}],"author":[{"full_name":"Draganić, Nemanja","last_name":"Draganić","first_name":"Nemanja"},{"id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","first_name":"Kalina H","full_name":"Petrova, Kalina H","last_name":"Petrova"}],"acknowledgement":"We would like to thank Rajko Nenadov and Miloš Trujić for helpful comments and discussions, as well as the anonymous referees for their very useful feedback, which improved the paper considerably. This research was supported by SNSF Project 217926. Part of this research was conducted while Nemanja Draganić was at ETH Zürich, Switzerland, and partially supported by SNSF Grant 200021_196965. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement Number: 101034413. Part of this research was conducted while Kalina Petrova was at the Department of Computer Science, ETH Zürich, Switzerland, supported by SNSF Grant CRSII5 173721.","intvolume":"       111","ddc":["510"],"scopus_import":"1","publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"file":[{"relation":"main_file","date_created":"2025-03-20T09:46:20Z","creator":"dernst","file_size":625974,"access_level":"open_access","file_name":"2025_JournLondonMath_Draganic.pdf","date_updated":"2025-03-20T09:46:20Z","success":1,"checksum":"d8e0a03286a44c4f672709e3c829206e","file_id":"19427","content_type":"application/pdf"}],"publisher":"Wiley","quality_controlled":"1","abstract":[{"text":"The size-Ramsey number r^(H) of a graph H is the smallest number of edges a (host) graph G can have, such that for any red/blue colouring of G, there is a monochromatic copy of H in G. Recently, Conlon, Nenadov and Trujić showed that if H is a graph on n vertices and maximum degree three, then r^(H)=O(n8/5), improving upon the upper bound of n5/3+o(1) by Kohayakawa, Rödl, Schacht and Szemerédi. In this paper we show that r^(H)≤n3/2+o(1). While the previously used host graphs were vanilla binomial random graphs, we prove our result using a novel host graph construction. Our bound hits a natural barrier of the existing methods.","lang":"eng"}],"title":"Size‐Ramsey numbers of graphs with maximum degree three","oa":1,"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"doi":"10.1112/jlms.70116","status":"public","date_updated":"2025-09-30T11:05:07Z","arxiv":1,"file_date_updated":"2025-03-20T09:46:20Z","year":"2025","date_published":"2025-03-01T00:00:00Z","_id":"19418","external_id":{"isi":["001450645400019"],"arxiv":["2207.05048"]},"date_created":"2025-03-19T09:03:37Z","publication":"Journal of the London Mathematical Society","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"No","day":"01"},{"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","oa":1,"arxiv":1,"doi":"10.1017/fms.2024.144","status":"public","date_updated":"2025-09-30T11:18:57Z","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"},{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics","grant_number":"101076777"}],"publication_identifier":{"issn":["2050-5094"]},"abstract":[{"lang":"eng","text":"An ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders. The theory of ordered 2-matchings is well developed and has connections and applications to extremal and enumerative combinatorics, probability and geometry. On the other hand, in the case  r≥3 much less is known, largely due to a lack of powerful bijective tools. Recently, Dudek, Grytczuk and Ruciński made some first steps towards a general theory of ordered r-matchings, and in this paper we substantially improve several of their results and introduce some new directions of study. Many intriguing open questions remain."}],"title":"Extremal, enumerative and probabilistic results on ordered hypergraph matchings","quality_controlled":"1","publisher":"Cambridge University Press","file":[{"date_updated":"2025-04-03T11:24:35Z","content_type":"application/pdf","checksum":"f396270ad78c1ed67095c8e5a66fca26","file_id":"19468","success":1,"file_size":630297,"access_level":"open_access","creator":"dernst","date_created":"2025-04-03T11:24:35Z","relation":"main_file","file_name":"2025_ForumMathSigma_Anastos.pdf"}],"type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"Forum of Mathematics, Sigma","day":"14","article_processing_charge":"Yes","year":"2025","file_date_updated":"2025-04-03T11:24:35Z","date_created":"2025-03-20T12:59:14Z","_id":"19433","external_id":{"arxiv":["2308.12268"],"isi":["001444429200001"]},"date_published":"2025-03-14T00:00:00Z","OA_place":"publisher","citation":{"ista":"Anastos M, Jin Z, Kwan MA, Sudakov B. 2025. Extremal, enumerative and probabilistic results on ordered hypergraph matchings. Forum of Mathematics, Sigma. 13, e55.","ieee":"M. Anastos, Z. Jin, M. A. Kwan, and B. Sudakov, “Extremal, enumerative and probabilistic results on ordered hypergraph matchings,” <i>Forum of Mathematics, Sigma</i>, vol. 13. Cambridge University Press, 2025.","chicago":"Anastos, Michael, Zhihan Jin, Matthew Alan Kwan, and Benny Sudakov. “Extremal, Enumerative and Probabilistic Results on Ordered Hypergraph Matchings.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/fms.2024.144\">https://doi.org/10.1017/fms.2024.144</a>.","mla":"Anastos, Michael, et al. “Extremal, Enumerative and Probabilistic Results on Ordered Hypergraph Matchings.” <i>Forum of Mathematics, Sigma</i>, vol. 13, e55, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/fms.2024.144\">10.1017/fms.2024.144</a>.","short":"M. Anastos, Z. Jin, M.A. Kwan, B. Sudakov, Forum of Mathematics, Sigma 13 (2025).","ama":"Anastos M, Jin Z, Kwan MA, Sudakov B. Extremal, enumerative and probabilistic results on ordered hypergraph matchings. <i>Forum of Mathematics, Sigma</i>. 2025;13. doi:<a href=\"https://doi.org/10.1017/fms.2024.144\">10.1017/fms.2024.144</a>","apa":"Anastos, M., Jin, Z., Kwan, M. A., &#38; Sudakov, B. (2025). Extremal, enumerative and probabilistic results on ordered hypergraph matchings. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.144\">https://doi.org/10.1017/fms.2024.144</a>"},"corr_author":"1","article_number":"e55","OA_type":"gold","has_accepted_license":"1","ec_funded":1,"department":[{"_id":"MaKw"}],"author":[{"last_name":"Anastos","full_name":"Anastos, Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","first_name":"Michael"},{"first_name":"Zhihan","full_name":"Jin, Zhihan","last_name":"Jin"},{"first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","last_name":"Kwan","full_name":"Kwan, Matthew Alan"},{"last_name":"Sudakov","full_name":"Sudakov, Benny","first_name":"Benny"}],"publication_status":"published","isi":1,"month":"03","volume":13,"scopus_import":"1","intvolume":"        13","ddc":["510"],"acknowledgement":"We would like to thank Timo Seppäläinen for some illuminating discussion about random high-dimensional orders and for bringing our attention to [59]. We would also like to thank the referees for helpful feedback. Michael Anastos is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101034413. Matthew Kwan is supported by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777, also funded by the European Union. Zhihan Jin and Benny Sudakov are supported by SNSF grant 200021-228014.","language":[{"iso":"eng"}],"oa_version":"Published Version"},{"oa_version":"Published Version","language":[{"iso":"eng"}],"month":"03","volume":66,"author":[{"last_name":"Alon","full_name":"Alon, Yahav","first_name":"Yahav"},{"id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","first_name":"Michael","last_name":"Anastos","full_name":"Anastos, Michael"}],"department":[{"_id":"MaKw"}],"isi":1,"publication_status":"published","acknowledgement":"The authors would like to express their thanks to the referees of the article for their valuable input towards improving the presentation of our result. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.","scopus_import":"1","intvolume":"        66","ddc":["510"],"OA_type":"hybrid","issue":"2","citation":{"chicago":"Alon, Yahav, and Michael Anastos. “The Completion Numbers of Hamiltonicity and Pancyclicity in Random Graphs.” <i>Random Structures and Algorithms</i>. Wiley, 2025. <a href=\"https://doi.org/10.1002/rsa.21286\">https://doi.org/10.1002/rsa.21286</a>.","ieee":"Y. Alon and M. Anastos, “The completion numbers of hamiltonicity and pancyclicity in random graphs,” <i>Random Structures and Algorithms</i>, vol. 66, no. 2. Wiley, 2025.","mla":"Alon, Yahav, and Michael Anastos. “The Completion Numbers of Hamiltonicity and Pancyclicity in Random Graphs.” <i>Random Structures and Algorithms</i>, vol. 66, no. 2, e21286, Wiley, 2025, doi:<a href=\"https://doi.org/10.1002/rsa.21286\">10.1002/rsa.21286</a>.","ista":"Alon Y, Anastos M. 2025. The completion numbers of hamiltonicity and pancyclicity in random graphs. Random Structures and Algorithms. 66(2), e21286.","ama":"Alon Y, Anastos M. The completion numbers of hamiltonicity and pancyclicity in random graphs. <i>Random Structures and Algorithms</i>. 2025;66(2). doi:<a href=\"https://doi.org/10.1002/rsa.21286\">10.1002/rsa.21286</a>","apa":"Alon, Y., &#38; Anastos, M. (2025). The completion numbers of hamiltonicity and pancyclicity in random graphs. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.21286\">https://doi.org/10.1002/rsa.21286</a>","short":"Y. Alon, M. Anastos, Random Structures and Algorithms 66 (2025)."},"article_number":"e21286","ec_funded":1,"has_accepted_license":"1","OA_place":"publisher","file_date_updated":"2025-03-25T11:46:27Z","year":"2025","_id":"19440","external_id":{"arxiv":["2304.03710"],"isi":["001420226800001"]},"date_published":"2025-03-01T00:00:00Z","date_created":"2025-03-23T23:01:26Z","publication":"Random Structures and Algorithms","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","day":"01","article_processing_charge":"Yes (in subscription journal)","publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"file":[{"file_name":"2025_RandomStruc_Alon.pdf","relation":"main_file","date_created":"2025-03-25T11:46:27Z","creator":"dernst","file_size":549236,"access_level":"open_access","success":1,"checksum":"6067747e805fa356d560dc45f2a89918","file_id":"19459","content_type":"application/pdf","date_updated":"2025-03-25T11:46:27Z"}],"title":"The completion numbers of hamiltonicity and pancyclicity in random graphs","abstract":[{"text":"Let μ(G) denote the minimum number of edges whose addition to G results in a Hamiltonian graph, and let μ^(G) denote the minimum number of edges whose addition to G results in a pancyclic graph. We study the distributions of μ(G),μ^(G) in the context of binomial random graphs. Letting d=d(n):=n⋅p, we prove that there exists a function f:R+→[0,1] of order f(d)=12de−d+e−d+O(d6e−3d) such that, if G∼G(n,p) with 20≤d(n)≤0.4logn, then with high probability μ(G)=(1+o(1))⋅f(d)⋅n. Let ni(G) denote the number of degree i vertices in G. A trivial lower bound on μ(G) is given by the expression n0(G)+⌈12n1(G)⌉. In the denser regime of random graphs, we show that if np−13logn−2loglogn→∞ and G∼G(n,p) then, with high probability, μ(G)=n0(G)+⌈12n1(G)⌉. For completion to pancyclicity, we show that if G∼G(n,p) and np≥20 then, with high probability, μ^(G)=μ(G). Finally, we present a polynomial time algorithm such that, if G∼G(n,p) and np≥20, then, with high probability, the algorithm returns a set of edges of size μ(G) whose addition to G results in a pancyclic (and therefore also Hamiltonian) graph.","lang":"eng"}],"quality_controlled":"1","publisher":"Wiley","oa":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)","image":"/images/cc_by_nc.png"},"doi":"10.1002/rsa.21286","status":"public","date_updated":"2025-09-30T11:15:41Z","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"arxiv":1},{"OA_place":"publisher","has_accepted_license":"1","ec_funded":1,"citation":{"chicago":"Christoph, Micha, Kalina H Petrova, and Raphael Steiner. “A Note on Digraph Splitting.” <i>Combinatorics Probability and Computing</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/S0963548325000045\">https://doi.org/10.1017/S0963548325000045</a>.","ieee":"M. Christoph, K. H. Petrova, and R. Steiner, “A note on digraph splitting,” <i>Combinatorics Probability and Computing</i>, vol. 34, no. 4. Cambridge University Press, pp. 559–564, 2025.","mla":"Christoph, Micha, et al. “A Note on Digraph Splitting.” <i>Combinatorics Probability and Computing</i>, vol. 34, no. 4, Cambridge University Press, 2025, pp. 559–64, doi:<a href=\"https://doi.org/10.1017/S0963548325000045\">10.1017/S0963548325000045</a>.","ista":"Christoph M, Petrova KH, Steiner R. 2025. A note on digraph splitting. Combinatorics Probability and Computing. 34(4), 559–564.","ama":"Christoph M, Petrova KH, Steiner R. A note on digraph splitting. <i>Combinatorics Probability and Computing</i>. 2025;34(4):559-564. doi:<a href=\"https://doi.org/10.1017/S0963548325000045\">10.1017/S0963548325000045</a>","apa":"Christoph, M., Petrova, K. H., &#38; Steiner, R. (2025). A note on digraph splitting. <i>Combinatorics Probability and Computing</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0963548325000045\">https://doi.org/10.1017/S0963548325000045</a>","short":"M. Christoph, K.H. Petrova, R. Steiner, Combinatorics Probability and Computing 34 (2025) 559–564."},"OA_type":"hybrid","issue":"4","scopus_import":"1","intvolume":"        34","ddc":["510"],"acknowledgement":"Funded by SNSF Ambizione grant No. 216071. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No, 101034413. Funded by SNSF grant CRSII5, 173721.","department":[{"_id":"MaKw"}],"author":[{"full_name":"Christoph, Micha","last_name":"Christoph","first_name":"Micha"},{"id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","first_name":"Kalina H","last_name":"Petrova","full_name":"Petrova, Kalina H"},{"first_name":"Raphael","full_name":"Steiner, Raphael","last_name":"Steiner"}],"publication_status":"published","isi":1,"volume":34,"month":"07","language":[{"iso":"eng"}],"oa_version":"Published Version","page":"559-564","arxiv":1,"status":"public","doi":"10.1017/S0963548325000045","date_updated":"2025-09-30T11:26:00Z","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020"}],"article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"quality_controlled":"1","title":"A note on digraph splitting","abstract":[{"lang":"eng","text":"A tantalizing open problem, posed independently by Stiebitz in 1995 and by Alon in 1996 and again in 2006, asks whether for every pair of integers  s,t≥1 there exists a finite number  F(s,t)\r\nsuch that the vertex set of every digraph of minimum out-degree at least  F(s,t) can be partitioned into non-empty parts  A  and  B  such that the subdigraphs induced on  A\r\n  and  B  have minimum out-degree at least  s  and  t , respectively.\r\nIn this short note, we prove that if  F(2,2)  exists, then all the numbers  F(s,t)  with  s,t≥1\r\n  exist and satisfy  F(s,t)=Θ(s+t) . In consequence, the problem of Alon and Stiebitz reduces to the case  s=t=2 . Moreover, the numbers  F(s,t)  with  s,t≥2  either all exist and grow linearly, or all of them do not exist."}],"publisher":"Cambridge University Press","file":[{"date_updated":"2025-08-05T12:54:06Z","checksum":"98491e59b4f0d05d69f608bbd5706f1a","file_id":"20135","content_type":"application/pdf","success":1,"access_level":"open_access","creator":"dernst","file_size":188818,"relation":"main_file","date_created":"2025-08-05T12:54:06Z","file_name":"2025_CombProbComputing_Christoph.pdf"}],"publication_identifier":{"eissn":["1469-2163"],"issn":["0963-5483"]},"day":"01","article_processing_charge":"Yes (in subscription journal)","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","publication":"Combinatorics Probability and Computing","date_created":"2025-04-06T22:01:32Z","_id":"19503","external_id":{"isi":["001449245700001"],"arxiv":["2310.08449"]},"date_published":"2025-07-01T00:00:00Z","year":"2025","file_date_updated":"2025-08-05T12:54:06Z"},{"file":[{"success":1,"checksum":"69ce9feaf64e776b99f3afd1041b1b11","content_type":"application/pdf","file_id":"19564","date_updated":"2025-04-15T13:18:43Z","file_name":"2025_JourLondMathSoc_Glasgow.pdf","relation":"main_file","date_created":"2025-04-15T13:18:43Z","access_level":"open_access","file_size":392208,"creator":"dernst"}],"publisher":"Wiley","quality_controlled":"1","title":"A central limit theorem for the matching number of a sparse random graph","abstract":[{"lang":"eng","text":"In 1981, Karp and Sipser proved a law of large numbers for the matching number of a sparse Erdős–Rényi random graph, in an influential paper pioneering the so-called differential equation method for analysis of random graph processes. Strengthening this classical result, and answering a question of Aronson, Frieze and Pittel, we prove a central limit theorem in the same setting: the fluctuations in the matching number of a sparse random graph are asymptotically Gaussian. Our new contribution is to prove this central limit theorem in the subcritical and critical regimes, according to a celebrated algorithmic phase transition first observed by Karp and Sipser. Indeed, in the supercritical regime, a central limit theorem has recently been proved in the PhD thesis of Kreačić, using a stochastic generalisation of the differential equation method (comparing the so-called Karp–Sipser process to a system of stochastic differential equations). Our proof builds on these methods, and introduces new techniques to handle certain degeneracies present in the subcritical and critical cases. Curiously, our new techniques lead to a non-constructive result: we are able to characterise the fluctuations of the matching number around its mean, despite these fluctuations being much smaller than the error terms in our best estimates of the mean. We also prove a central limit theorem for the rank of the adjacency matrix of a sparse random graph."}],"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"status":"public","date_updated":"2025-09-30T11:35:55Z","doi":"10.1112/jlms.70101","arxiv":1,"oa":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)","image":"/images/cc_by_nc.png"},"date_published":"2025-04-01T00:00:00Z","_id":"19554","external_id":{"isi":["001473087200024"],"arxiv":["2402.05851"]},"date_created":"2025-04-13T22:01:19Z","file_date_updated":"2025-04-15T13:18:43Z","year":"2025","article_processing_charge":"Yes (via OA deal)","day":"01","publication":"Journal of the London Mathematical Society","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","has_accepted_license":"1","OA_type":"hybrid","issue":"4","corr_author":"1","article_number":"e70101","citation":{"short":"M. Glasgow, M.A. Kwan, A. Sah, M. Sawhney, Journal of the London Mathematical Society 111 (2025).","ama":"Glasgow M, Kwan MA, Sah A, Sawhney M. A central limit theorem for the matching number of a sparse random graph. <i>Journal of the London Mathematical Society</i>. 2025;111(4). doi:<a href=\"https://doi.org/10.1112/jlms.70101\">10.1112/jlms.70101</a>","apa":"Glasgow, M., Kwan, M. A., Sah, A., &#38; Sawhney, M. (2025). A central limit theorem for the matching number of a sparse random graph. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.70101\">https://doi.org/10.1112/jlms.70101</a>","ista":"Glasgow M, Kwan MA, Sah A, Sawhney M. 2025. A central limit theorem for the matching number of a sparse random graph. Journal of the London Mathematical Society. 111(4), e70101.","chicago":"Glasgow, Margalit, Matthew Alan Kwan, Ashwin Sah, and Mehtaab Sawhney. “A Central Limit Theorem for the Matching Number of a Sparse Random Graph.” <i>Journal of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/jlms.70101\">https://doi.org/10.1112/jlms.70101</a>.","ieee":"M. Glasgow, M. A. Kwan, A. Sah, and M. Sawhney, “A central limit theorem for the matching number of a sparse random graph,” <i>Journal of the London Mathematical Society</i>, vol. 111, no. 4. Wiley, 2025.","mla":"Glasgow, Margalit, et al. “A Central Limit Theorem for the Matching Number of a Sparse Random Graph.” <i>Journal of the London Mathematical Society</i>, vol. 111, no. 4, e70101, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/jlms.70101\">10.1112/jlms.70101</a>."},"OA_place":"publisher","oa_version":"Published Version","language":[{"iso":"eng"}],"acknowledgement":"We would like to thank Christina Goldschmidt and Eleonora Kreačić for insightful discussions and clarifications about their work in the thesis [26]. Matthew Kwan was supported by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777. Ashwin Sah and Mehtaab Sawhney were supported by NSF Graduate Research Fellowship Program DGE-2141064. Ashwin Sah was supported by the PD Soros Fellowship.\r\nOpen access funding provided by Institute of Science and Technology Austria/KEMÖ.","intvolume":"       111","ddc":["510"],"scopus_import":"1","month":"04","volume":111,"isi":1,"publication_status":"published","author":[{"full_name":"Glasgow, Margalit","last_name":"Glasgow","first_name":"Margalit"},{"orcid":"0000-0002-4003-7567","last_name":"Kwan","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"first_name":"Ashwin","full_name":"Sah, Ashwin","last_name":"Sah"},{"full_name":"Sawhney, Mehtaab","last_name":"Sawhney","first_name":"Mehtaab"}],"department":[{"_id":"MaKw"}]},{"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"doi":"10.1007/s00453-025-01306-y","date_updated":"2026-01-05T13:46:08Z","status":"public","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publisher":"Springer Nature","abstract":[{"text":"MaxCut is a classical NP-complete problem and a crucial building block in many\r\ncombinatorial algorithms. The famousEdwards-Erdös bound states that any connected\r\ngraph on n vertices with m edges contains a cut of size at least m/2 + n−1/4 . Crowston,\r\nJones and Mnich [Algorithmica, 2015] showed that the MaxCut problem on simple\r\nconnected graphs admits an FPT algorithm, where the parameter k is the difference\r\nbetween the desired cut size c and the lower bound given by the Edwards-Erdös\r\nbound. This was later improved by Etscheid and Mnich [Algorithmica, 2017] to run\r\nin parameterized linear time, i.e., f (k) · O(m). We improve upon this result in two\r\nways: Firstly, we extend the algorithm to work also for multigraphs (alternatively,\r\ngraphs with positive integer weights). Secondly, we change the parameter; instead of\r\nthe difference to the Edwards-Erdös bound, we use the difference to the Poljak-Turzík\r\nbound. The Poljak-Turzík bound states that any weighted graph G has a cut of weight\r\nat least w(G)/2 + wMSF (G)/4 , where w(G) denotes the total weight of G, and wMSF (G)\r\ndenotes the weight of its minimum spanning forest. In connected simple graphs the\r\ntwo bounds are equivalent, but for multigraphs the Poljak-Turzík bound can be larger\r\nand thus yield a smaller parameter k. Our algorithm also runs in parameterized linear\r\ntime, i.e., f (k) · O(m + n).","lang":"eng"}],"title":"Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound","quality_controlled":"1","file":[{"date_updated":"2026-01-05T13:45:57Z","content_type":"application/pdf","checksum":"eab3f1834b0ba347b05ae9897729c0ad","file_id":"20957","success":1,"access_level":"open_access","creator":"dernst","file_size":448554,"date_created":"2026-01-05T13:45:57Z","relation":"main_file","file_name":"2025_Algorithmica_Lill.pdf"}],"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"article_processing_charge":"Yes (via OA deal)","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","publication":"Algorithmica","date_created":"2025-04-20T22:01:28Z","date_published":"2025-07-01T00:00:00Z","_id":"19603","external_id":{"isi":["001463103800001"]},"year":"2025","file_date_updated":"2026-01-05T13:45:57Z","OA_place":"publisher","has_accepted_license":"1","ec_funded":1,"related_material":{"record":[{"status":"public","id":"18758","relation":"earlier_version"}]},"citation":{"ista":"Lill J, Petrova KH, Weber S. 2025. Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. Algorithmica. 87, 983–1007.","mla":"Lill, Jonas, et al. “Linear-Time MaxCut in Multigraphs Parameterized above the Poljak-Turzík Bound.” <i>Algorithmica</i>, vol. 87, Springer Nature, 2025, pp. 983–1007, doi:<a href=\"https://doi.org/10.1007/s00453-025-01306-y\">10.1007/s00453-025-01306-y</a>.","ieee":"J. Lill, K. H. Petrova, and S. Weber, “Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound,” <i>Algorithmica</i>, vol. 87. Springer Nature, pp. 983–1007, 2025.","chicago":"Lill, Jonas, Kalina H Petrova, and Simon Weber. “Linear-Time MaxCut in Multigraphs Parameterized above the Poljak-Turzík Bound.” <i>Algorithmica</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00453-025-01306-y\">https://doi.org/10.1007/s00453-025-01306-y</a>.","short":"J. Lill, K.H. Petrova, S. Weber, Algorithmica 87 (2025) 983–1007.","apa":"Lill, J., Petrova, K. H., &#38; Weber, S. (2025). Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-025-01306-y\">https://doi.org/10.1007/s00453-025-01306-y</a>","ama":"Lill J, Petrova KH, Weber S. Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. <i>Algorithmica</i>. 2025;87:983-1007. doi:<a href=\"https://doi.org/10.1007/s00453-025-01306-y\">10.1007/s00453-025-01306-y</a>"},"OA_type":"hybrid","intvolume":"        87","ddc":["510"],"scopus_import":"1","acknowledgement":"Kalina Petrova is supported by the Swiss National Science Foundation, grant no. CRSII5 173721, and also receives funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. Simon Weber is supported by the Swiss National Science Foundation under project no. 204320.\r\nOpen access funding provided by Swiss Federal Institute of Technology Zurich.","publication_status":"published","isi":1,"author":[{"first_name":"Jonas","last_name":"Lill","full_name":"Lill, Jonas"},{"last_name":"Petrova","full_name":"Petrova, Kalina H","first_name":"Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381"},{"full_name":"Weber, Simon","last_name":"Weber","first_name":"Simon"}],"department":[{"_id":"MaKw"}],"volume":87,"month":"07","language":[{"iso":"eng"}],"page":"983-1007","oa_version":"Published Version"},{"issue":"9","OA_type":"green","citation":{"ista":"Anastos M, Morris P. 2025. A note on finding large transversals efficiently. Journal of Combinatorial Designs. 33(9), 338–342.","mla":"Anastos, Michael, and Patrick Morris. “A Note on Finding Large Transversals Efficiently.” <i>Journal of Combinatorial Designs</i>, vol. 33, no. 9, Wiley, 2025, pp. 338–42, doi:<a href=\"https://doi.org/10.1002/jcd.21990\">10.1002/jcd.21990</a>.","ieee":"M. Anastos and P. Morris, “A note on finding large transversals efficiently,” <i>Journal of Combinatorial Designs</i>, vol. 33, no. 9. Wiley, pp. 338–342, 2025.","chicago":"Anastos, Michael, and Patrick Morris. “A Note on Finding Large Transversals Efficiently.” <i>Journal of Combinatorial Designs</i>. Wiley, 2025. <a href=\"https://doi.org/10.1002/jcd.21990\">https://doi.org/10.1002/jcd.21990</a>.","short":"M. Anastos, P. Morris, Journal of Combinatorial Designs 33 (2025) 338–342.","apa":"Anastos, M., &#38; Morris, P. (2025). A note on finding large transversals efficiently. <i>Journal of Combinatorial Designs</i>. Wiley. <a href=\"https://doi.org/10.1002/jcd.21990\">https://doi.org/10.1002/jcd.21990</a>","ama":"Anastos M, Morris P. A note on finding large transversals efficiently. <i>Journal of Combinatorial Designs</i>. 2025;33(9):338-342. doi:<a href=\"https://doi.org/10.1002/jcd.21990\">10.1002/jcd.21990</a>"},"ec_funded":1,"OA_place":"repository","page":"338-342","oa_version":"Preprint","language":[{"iso":"eng"}],"volume":33,"month":"09","isi":1,"publication_status":"published","department":[{"_id":"MaKw"}],"author":[{"last_name":"Anastos","full_name":"Anastos, Michael","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","first_name":"Michael"},{"full_name":"Morris, Patrick","last_name":"Morris","first_name":"Patrick"}],"acknowledgement":"We are very grateful to Matthew Kwan and Alp Müyesser with whom we had many interesting discussions leading to the results of this note. We also thank the anonymous reviewers for their suggestions improving the presentation of this note.\r\n\r\nMA was supported by the Austrian Science Fund (FWF) [10.55776/ESP3863424] and by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant—project number 101034413. PM was supported by the European Union's Horizon Europe Marie Skłodowska-Curie grant RAND-COMB-DESIGN—project number 101106032.","intvolume":"        33","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.05891","open_access":"1"}],"publication_identifier":{"eissn":["1520-6610"],"issn":["1063-8539"]},"publisher":"Wiley","abstract":[{"text":"In an  n×n  array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than  βn  times, the array contains a transversal of size  (1−β/4−o(1))n . In particular, if the array is filled with  n  symbols, each appearing  n  times (an equi- n  square), we get transversals of size  (3/4−o(1))n. Moreover, our proof gives a deterministic algorithm with polynomial running time, that finds these transversals.","lang":"eng"}],"title":"A note on finding large transversals efficiently","quality_controlled":"1","oa":1,"article_type":"original","project":[{"name":"Combinatorial Optimisation Problems on Sparse Random Graphs","grant_number":"ESP3863424","_id":"8f906bd2-16d5-11f0-9cad-e07be8aa9ac9"},{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"status":"public","doi":"10.1002/jcd.21990","date_updated":"2025-12-30T08:37:37Z","arxiv":1,"year":"2025","date_published":"2025-09-01T00:00:00Z","external_id":{"isi":["001495472300001"],"arxiv":["2412.05891"]},"_id":"19798","date_created":"2025-06-08T22:01:23Z","publication":"Journal of Combinatorial Designs","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","article_processing_charge":"No","day":"01"},{"publisher":"École normale supérieure de Rennes","abstract":[{"lang":"eng","text":"We consider a recently introduced model of color-avoiding percolation (abbreviated CA-percolation) defined as follows. Every edge in a graph G is colored in some of k>=2 colors. Two vertices u and v in G are said to be CA-connected if u and v may be connected using any subset of k-1 colors. CA-connectivity defines an equivalence relation on the vertex set of G whose classes are called CA-components.\r\nWe study the component structure of a randomly colored Erdős–Rényi random graph of constant average degree. We distinguish three regimes for the size of the largest component: a supercritical regime, a so-called intermediate regime, and a subcritical regime, in which the largest CA-component has respectively linear, logarithmic, and bounded size. Interestingly, in the subcritical regime, the bound is deterministic and given by the number of colors."}],"title":"Color-avoiding percolation on the Erdős–Rényi random graph","quality_controlled":"1","file":[{"file_name":"2025_AnnalesHenriLebesgue_Lichev.pdf","file_size":746588,"creator":"dernst","access_level":"open_access","date_created":"2025-06-23T11:59:22Z","relation":"main_file","checksum":"cca22d171b7affa010d17f5e793b0045","content_type":"application/pdf","file_id":"19875","success":1,"date_updated":"2025-06-23T11:59:22Z"}],"publication_identifier":{"eissn":["2644-9463"]},"arxiv":1,"DOAJ_listed":"1","status":"public","date_updated":"2025-06-23T12:01:36Z","doi":"10.5802/ahl.228","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"date_created":"2025-06-22T22:02:07Z","date_published":"2025-06-01T00:00:00Z","_id":"19859","external_id":{"arxiv":["2211.16086 "]},"year":"2025","file_date_updated":"2025-06-23T11:59:22Z","article_processing_charge":"Yes","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","publication":"Annales Henri Lebesgue","has_accepted_license":"1","corr_author":"1","citation":{"short":"L. Lichev, B. Schapira, Annales Henri Lebesgue 8 (2025) 35–65.","ama":"Lichev L, Schapira B. Color-avoiding percolation on the Erdős–Rényi random graph. <i>Annales Henri Lebesgue</i>. 2025;8:35-65. doi:<a href=\"https://doi.org/10.5802/ahl.228\">10.5802/ahl.228</a>","apa":"Lichev, L., &#38; Schapira, B. (2025). Color-avoiding percolation on the Erdős–Rényi random graph. <i>Annales Henri Lebesgue</i>. École normale supérieure de Rennes. <a href=\"https://doi.org/10.5802/ahl.228\">https://doi.org/10.5802/ahl.228</a>","ista":"Lichev L, Schapira B. 2025. Color-avoiding percolation on the Erdős–Rényi random graph. Annales Henri Lebesgue. 8, 35–65.","ieee":"L. Lichev and B. Schapira, “Color-avoiding percolation on the Erdős–Rényi random graph,” <i>Annales Henri Lebesgue</i>, vol. 8. École normale supérieure de Rennes, pp. 35–65, 2025.","chicago":"Lichev, Lyuben, and Bruno Schapira. “Color-Avoiding Percolation on the Erdős–Rényi Random Graph.” <i>Annales Henri Lebesgue</i>. École normale supérieure de Rennes, 2025. <a href=\"https://doi.org/10.5802/ahl.228\">https://doi.org/10.5802/ahl.228</a>.","mla":"Lichev, Lyuben, and Bruno Schapira. “Color-Avoiding Percolation on the Erdős–Rényi Random Graph.” <i>Annales Henri Lebesgue</i>, vol. 8, École normale supérieure de Rennes, 2025, pp. 35–65, doi:<a href=\"https://doi.org/10.5802/ahl.228\">10.5802/ahl.228</a>."},"OA_type":"gold","OA_place":"publisher","language":[{"iso":"eng"}],"page":"35-65","oa_version":"Published Version","ddc":["510"],"intvolume":"         8","scopus_import":"1","acknowledgement":"We thank Dieter Mitsche for enlightening discussions, Balázs Ráth for a number of comments\r\nand corrections on a first version of this paper, and an anonymous referee for several useful remarks.","publication_status":"published","author":[{"full_name":"Lichev, Lyuben","last_name":"Lichev","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben"},{"first_name":"Bruno","full_name":"Schapira, Bruno","last_name":"Schapira"}],"department":[{"_id":"MaKw"}],"month":"06","volume":8}]