[{"date_updated":"2026-02-16T09:55:17Z","file_date_updated":"2026-02-16T09:52:38Z","file":[{"date_updated":"2026-02-16T09:52:38Z","file_size":539646,"file_id":"21228","content_type":"application/pdf","relation":"main_file","file_name":"2026_Combinatorica_Kwan.pdf","creator":"dernst","success":1,"date_created":"2026-02-16T09:52:38Z","checksum":"47b0031d90b0e6b9a843f422a1486089","access_level":"open_access"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":46,"year":"2026","publication_status":"published","_id":"21159","oa_version":"Published Version","article_type":"original","oa":1,"author":[{"last_name":"Kwan","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan"},{"first_name":"Roodabeh","last_name":"Safavi Hemami","full_name":"Safavi Hemami, Roodabeh","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154"},{"first_name":"Yiting","last_name":"Wang","orcid":"0000-0002-2856-767X","full_name":"Wang, Yiting","id":"1917d194-076e-11ed-97cd-837255f88785"}],"external_id":{"arxiv":["2408.09589"]},"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"}],"PlanS_conform":"1","department":[{"_id":"MaKw"},{"_id":"MoHe"}],"OA_type":"hybrid","title":"Counting perfect matchings in Dirac hypergraphs","corr_author":"1","ddc":["510"],"scopus_import":"1","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"status":"public","has_accepted_license":"1","date_created":"2026-02-08T23:02:49Z","doi":"10.1007/s00493-025-00194-8","arxiv":1,"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).","type":"journal_article","day":"01","article_number":"5","intvolume":"        46","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2026-02-01T00:00:00Z","citation":{"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>","short":"M.A. Kwan, R. Safavi Hemami, Y. Wang, Combinatorica 46 (2026).","ieee":"M. A. Kwan, R. Safavi Hemami, and Y. Wang, “Counting perfect matchings in Dirac hypergraphs,” <i>Combinatorica</i>, vol. 46. Springer Nature, 2026.","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>.","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>","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>."},"publication":"Combinatorica","article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","language":[{"iso":"eng"}],"OA_place":"publisher","publisher":"Springer Nature","month":"02"},{"article_type":"original","page":"803-813","oa":1,"_id":"15275","oa_version":"Preprint","department":[{"_id":"HeEd"}],"external_id":{"arxiv":["1912.02342"]},"author":[{"full_name":"Fox, Jacob","first_name":"Jacob","last_name":"Fox"},{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","last_name":"Pach","first_name":"János"},{"last_name":"Suk","first_name":"Andrew","full_name":"Suk, Andrew"}],"abstract":[{"lang":"eng","text":"In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum integer n > 1 such that for any m-coloring of the edges of the complete graph Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings with bounded VC-dimension, that is, for m-colorings with the property that the set system induced by the neighborhoods of the vertices with respect to each color class has bounded VC-dimension."}],"date_updated":"2024-04-09T10:40:08Z","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"volume":41,"year":"2021","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Fox, Jacob, et al. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” <i>Combinatorica</i>, vol. 41, no. 6, Springer Nature, 2021, pp. 803–13, doi:<a href=\"https://doi.org/10.1007/s00493-021-4530-9\">10.1007/s00493-021-4530-9</a>.","ama":"Fox J, Pach J, Suk A. Bounded VC-dimension implies the Schur-Erdős conjecture. <i>Combinatorica</i>. 2021;41(6):803-813. doi:<a href=\"https://doi.org/10.1007/s00493-021-4530-9\">10.1007/s00493-021-4530-9</a>","ieee":"J. Fox, J. Pach, and A. Suk, “Bounded VC-dimension implies the Schur-Erdős conjecture,” <i>Combinatorica</i>, vol. 41, no. 6. Springer Nature, pp. 803–813, 2021.","chicago":"Fox, Jacob, János Pach, and Andrew Suk. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” <i>Combinatorica</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00493-021-4530-9\">https://doi.org/10.1007/s00493-021-4530-9</a>.","short":"J. Fox, J. Pach, A. Suk, Combinatorica 41 (2021) 803–813.","ista":"Fox J, Pach J, Suk A. 2021. Bounded VC-dimension implies the Schur-Erdős conjecture. Combinatorica. 41(6), 803–813.","apa":"Fox, J., Pach, J., &#38; Suk, A. (2021). Bounded VC-dimension implies the Schur-Erdős conjecture. <i>Combinatorica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00493-021-4530-9\">https://doi.org/10.1007/s00493-021-4530-9</a>"},"date_published":"2021-11-20T00:00:00Z","intvolume":"        41","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"11","publication":"Combinatorica","quality_controlled":"1","article_processing_charge":"No","publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"issue":"6","title":"Bounded VC-dimension implies the Schur-Erdős conjecture","type":"journal_article","day":"20","status":"public","arxiv":1,"doi":"10.1007/s00493-021-4530-9","date_created":"2024-04-03T07:59:57Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1912.02342"}]},{"extern":"1","abstract":[{"lang":"eng","text":"The problem of finding dense induced bipartite subgraphs in H-free graphs has a long history, and was posed 30 years ago by Erdős, Faudree, Pach and Spencer. In this paper, we obtain several results in this direction. First we prove that any H-free graph with minimum degree at least d contains an induced bipartite subgraph of minimum degree at least cH log d/log log d, thus nearly confirming one and proving another conjecture of Esperet, Kang and Thomassé. Complementing this result, we further obtain optimal bounds for this problem in the case of dense triangle-free graphs, and we also answer a question of Erdœs, Janson, Łuczak and Spencer."}],"external_id":{"arxiv":["1810.12144"]},"author":[{"first_name":"Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567","full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"full_name":"Letzter, Shoham","first_name":"Shoham","last_name":"Letzter"},{"first_name":"Benny","last_name":"Sudakov","full_name":"Sudakov, Benny"},{"full_name":"Tran, Tuan","last_name":"Tran","first_name":"Tuan"}],"oa_version":"Preprint","_id":"9582","oa":1,"page":"283-305","article_type":"original","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","publication_status":"published","volume":40,"year":"2020","date_updated":"2023-02-23T14:01:45Z","quality_controlled":"1","article_processing_charge":"No","publication":"Combinatorica","month":"04","publisher":"Springer","language":[{"iso":"eng"}],"intvolume":"        40","citation":{"ama":"Kwan MA, Letzter S, Sudakov B, Tran T. Dense induced bipartite subgraphs in triangle-free graphs. <i>Combinatorica</i>. 2020;40(2):283-305. doi:<a href=\"https://doi.org/10.1007/s00493-019-4086-0\">10.1007/s00493-019-4086-0</a>","ieee":"M. A. Kwan, S. Letzter, B. Sudakov, and T. Tran, “Dense induced bipartite subgraphs in triangle-free graphs,” <i>Combinatorica</i>, vol. 40, no. 2. Springer, pp. 283–305, 2020.","chicago":"Kwan, Matthew Alan, Shoham Letzter, Benny Sudakov, and Tuan Tran. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” <i>Combinatorica</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s00493-019-4086-0\">https://doi.org/10.1007/s00493-019-4086-0</a>.","mla":"Kwan, Matthew Alan, et al. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” <i>Combinatorica</i>, vol. 40, no. 2, Springer, 2020, pp. 283–305, doi:<a href=\"https://doi.org/10.1007/s00493-019-4086-0\">10.1007/s00493-019-4086-0</a>.","ista":"Kwan MA, Letzter S, Sudakov B, Tran T. 2020. Dense induced bipartite subgraphs in triangle-free graphs. Combinatorica. 40(2), 283–305.","apa":"Kwan, M. A., Letzter, S., Sudakov, B., &#38; Tran, T. (2020). Dense induced bipartite subgraphs in triangle-free graphs. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/s00493-019-4086-0\">https://doi.org/10.1007/s00493-019-4086-0</a>","short":"M.A. Kwan, S. Letzter, B. Sudakov, T. Tran, Combinatorica 40 (2020) 283–305."},"date_published":"2020-04-01T00:00:00Z","date_created":"2021-06-22T06:42:26Z","main_file_link":[{"url":"https://arxiv.org/abs/1810.12144","open_access":"1"}],"arxiv":1,"doi":"10.1007/s00493-019-4086-0","status":"public","day":"01","type":"journal_article","issue":"2","title":"Dense induced bipartite subgraphs in triangle-free graphs","scopus_import":"1","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]}},{"abstract":[{"lang":"eng","text":"We find a graph of genus 5 and its drawing on the orientable surface of genus 4 with every pair of independent edges crossing an even number of times. This shows that the strong Hanani–Tutte theorem cannot be extended to the orientable surface of genus 4. As a base step in the construction we use a counterexample to an extension of the unified Hanani–Tutte theorem on the torus."}],"author":[{"last_name":"Fulek","first_name":"Radoslav","id":"39F3FFE4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8485-1774","full_name":"Fulek, Radoslav"},{"first_name":"Jan","last_name":"Kynčl","full_name":"Kynčl, Jan"}],"external_id":{"arxiv":["1709.00508"],"isi":["000493267200003"]},"department":[{"_id":"UlWa"}],"oa_version":"Preprint","ec_funded":1,"_id":"7034","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"261FA626-B435-11E9-9278-68D0E5697425","grant_number":"M02281","call_identifier":"FWF","name":"Eliminating intersections in drawings of graphs"}],"oa":1,"page":"1267-1279","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"publication_status":"published","volume":39,"year":"2019","date_updated":"2025-04-14T13:52:37Z","article_processing_charge":"No","quality_controlled":"1","publication":"Combinatorica","month":"10","language":[{"iso":"eng"}],"publisher":"Springer Nature","intvolume":"        39","date_published":"2019-10-29T00:00:00Z","citation":{"chicago":"Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” <i>Combinatorica</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00493-019-3905-7\">https://doi.org/10.1007/s00493-019-3905-7</a>.","ieee":"R. Fulek and J. Kynčl, “Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4,” <i>Combinatorica</i>, vol. 39, no. 6. Springer Nature, pp. 1267–1279, 2019.","ama":"Fulek R, Kynčl J. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. <i>Combinatorica</i>. 2019;39(6):1267-1279. doi:<a href=\"https://doi.org/10.1007/s00493-019-3905-7\">10.1007/s00493-019-3905-7</a>","mla":"Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4.” <i>Combinatorica</i>, vol. 39, no. 6, Springer Nature, 2019, pp. 1267–79, doi:<a href=\"https://doi.org/10.1007/s00493-019-3905-7\">10.1007/s00493-019-3905-7</a>.","apa":"Fulek, R., &#38; Kynčl, J. (2019). Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. <i>Combinatorica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00493-019-3905-7\">https://doi.org/10.1007/s00493-019-3905-7</a>","ista":"Fulek R, Kynčl J. 2019. Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4. Combinatorica. 39(6), 1267–1279.","short":"R. Fulek, J. Kynčl, Combinatorica 39 (2019) 1267–1279."},"date_created":"2019-11-18T14:29:50Z","main_file_link":[{"url":"https://arxiv.org/abs/1709.00508","open_access":"1"}],"doi":"10.1007/s00493-019-3905-7","arxiv":1,"status":"public","type":"journal_article","day":"29","title":"Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4","issue":"6","publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"scopus_import":"1"},{"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"}],"extern":"1","abstract":[{"text":"Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.","lang":"eng"}],"article_type":"original","page":"251 - 260","_id":"4069","oa_version":"None","year":"1990","volume":10,"publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-21T11:08:30Z","publisher":"Springer","language":[{"iso":"eng"}],"month":"09","publication":"Combinatorica","quality_controlled":"1","article_processing_charge":"No","citation":{"ieee":"H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” <i>Combinatorica</i>, vol. 10, no. 3. Springer, pp. 251–260, 1990.","chicago":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>.","ama":"Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. 1990;10(3):251-260. doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>","mla":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>.","ista":"Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 10(3), 251–260.","apa":"Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>","short":"H. Edelsbrunner, Combinatorica 10 (1990) 251–260."},"date_published":"1990-09-01T00:00:00Z","intvolume":"        10","acknowledgement":"Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565.","day":"01","type":"journal_article","status":"public","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02122779"}],"doi":"10.1007/BF02122779","date_created":"2018-12-11T12:06:45Z","publist_id":"2050","scopus_import":"1","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"issue":"3","title":"An acyclicity theorem for cell complexes in d dimension"}]