[{"title":"Off-diagonal Ramsey numbers for linear hypergraphs","_id":"22152","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.1017/s0963548326100443","publication_identifier":{"issn":["0963-5483"],"eissn":["1469-2163"]},"page":"1-14","day":"14","arxiv":1,"doi":"10.1017/s0963548326100443","oa":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"mathsc":["05D10","05D40","05C65"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/S0963548326100443"}],"article_processing_charge":"No","external_id":{"arxiv":["2507.05641"]},"article_type":"original","abstract":[{"lang":"eng","text":"We study off-diagonal Ramsey numbers 𝑟⁡(𝐻,𝐾(𝑘)\r\n𝑛) of 𝑘-uniform hypergraphs, where 𝐻 is a fixed linear 𝑘-uniform hypergraph and 𝐾(𝑘)\r\n𝑛 is complete on 𝑛 vertices. Recently, Conlon, Fox, Gunby, He, Mubayi, Suk, and Verstraëte disproved the folklore conjecture that 𝑟⁡(𝐻,𝐾(3)\r\n𝑛) always grows polynomially in 𝑛. In this paper, we show that much larger growth rates are possible in higher uniformity. In uniformity 𝑘 ≥4, we prove that for any constant 𝐶 >0, there exists a linear 𝑘-uniform hypergraph 𝐻 for which\r\n\r\n𝑟⁡(𝐻,𝐾(𝑘)\r\n𝑛)≥twr𝑘−2⁢(2(log⁡𝑛)𝐶)."}],"language":[{"iso":"eng"}],"type":"journal_article","OA_place":"publisher","status":"public","quality_controlled":"1","date_updated":"2026-07-08T07:24:54Z","OA_type":"hybrid","scopus_import":"1","author":[{"full_name":"He, Xiaoyu","first_name":"Xiaoyu","last_name":"He"},{"first_name":"Jiaxi","last_name":"Nie","full_name":"Nie, Jiaxi"},{"full_name":"Wigderson, Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","first_name":"Yuval"},{"full_name":"Yu, Hung-Hsun","first_name":"Hung-Hsun","last_name":"Yu"}],"publication":"Combinatorics, Probability and Computing","date_created":"2026-06-29T10:47:02Z","year":"2026","publication_status":"epub_ahead","citation":{"apa":"He, X., Nie, J., Wigderson, Y., &#38; Yu, H.-H. (2026). Off-diagonal Ramsey numbers for linear hypergraphs. <i>Combinatorics, Probability and Computing</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0963548326100443\">https://doi.org/10.1017/s0963548326100443</a>","mla":"He, Xiaoyu, et al. “Off-Diagonal Ramsey Numbers for Linear Hypergraphs.” <i>Combinatorics, Probability and Computing</i>, Cambridge University Press, 2026, pp. 1–14, doi:<a href=\"https://doi.org/10.1017/s0963548326100443\">10.1017/s0963548326100443</a>.","chicago":"He, Xiaoyu, Jiaxi Nie, Yuval Wigderson, and Hung-Hsun Yu. “Off-Diagonal Ramsey Numbers for Linear Hypergraphs.” <i>Combinatorics, Probability and Computing</i>. Cambridge University Press, 2026. <a href=\"https://doi.org/10.1017/s0963548326100443\">https://doi.org/10.1017/s0963548326100443</a>.","short":"X. He, J. Nie, Y. Wigderson, H.-H. Yu, Combinatorics, Probability and Computing (2026) 1–14.","ama":"He X, Nie J, Wigderson Y, Yu H-H. Off-diagonal Ramsey numbers for linear hypergraphs. <i>Combinatorics, Probability and Computing</i>. 2026:1-14. doi:<a href=\"https://doi.org/10.1017/s0963548326100443\">10.1017/s0963548326100443</a>","ista":"He X, Nie J, Wigderson Y, Yu H-H. 2026. Off-diagonal Ramsey numbers for linear hypergraphs. Combinatorics, Probability and Computing., 1–14.","ieee":"X. He, J. Nie, Y. Wigderson, and H.-H. Yu, “Off-diagonal Ramsey numbers for linear hypergraphs,” <i>Combinatorics, Probability and Computing</i>. Cambridge University Press, pp. 1–14, 2026."},"oa_version":"Published Version","date_published":"2026-04-14T00:00:00Z","extern":"1","month":"04","ddc":["500"],"publisher":"Cambridge University Press"},{"issue":"4","file":[{"relation":"main_file","date_updated":"2025-08-05T12:54:06Z","success":1,"access_level":"open_access","creator":"dernst","checksum":"98491e59b4f0d05d69f608bbd5706f1a","file_name":"2025_CombProbComputing_Christoph.pdf","file_size":188818,"date_created":"2025-08-05T12:54:06Z","file_id":"20135","content_type":"application/pdf"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"doi":"10.1017/S0963548325000045","oa":1,"has_accepted_license":"1","volume":34,"external_id":{"isi":["001449245700001"],"arxiv":["2310.08449"]},"article_type":"original","article_processing_charge":"Yes (in subscription journal)","_id":"19503","title":"A note on digraph splitting","ec_funded":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"MaKw"}],"fulldoi":"https://doi.org/10.1017/S0963548325000045","day":"01","page":"559-564","publication_identifier":{"eissn":["1469-2163"],"issn":["0963-5483"]},"arxiv":1,"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.","isi":1,"intvolume":"        34","file_date_updated":"2025-08-05T12:54:06Z","date_created":"2025-04-06T22:01:32Z","year":"2025","publication":"Combinatorics Probability and Computing","publication_status":"published","oa_version":"Published Version","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>.","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>.","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.","ista":"Christoph M, Petrova KH, Steiner R. 2025. A note on digraph splitting. Combinatorics Probability and Computing. 34(4), 559–564.","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.","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>"},"month":"07","ddc":["510"],"publisher":"Cambridge University Press","date_published":"2025-07-01T00:00:00Z","type":"journal_article","OA_place":"publisher","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"status":"public","quality_controlled":"1","date_updated":"2025-09-30T11:26:00Z","scopus_import":"1","OA_type":"hybrid","author":[{"last_name":"Christoph","first_name":"Micha","full_name":"Christoph, Micha"},{"full_name":"Petrova, Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","last_name":"Petrova","first_name":"Kalina H"},{"full_name":"Steiner, Raphael","first_name":"Raphael","last_name":"Steiner"}]},{"oa_version":"Preprint","citation":{"ista":"Conlon D, Fox J, Wigderson Y. 2023. Off-diagonal book Ramsey numbers. Combinatorics, Probability and Computing. 32(3), 516–545.","ieee":"D. Conlon, J. Fox, and Y. Wigderson, “Off-diagonal book Ramsey numbers,” <i>Combinatorics, Probability and Computing</i>, vol. 32, no. 3. Cambridge University Press, pp. 516–545, 2023.","ama":"Conlon D, Fox J, Wigderson Y. Off-diagonal book Ramsey numbers. <i>Combinatorics, Probability and Computing</i>. 2023;32(3):516-545. doi:<a href=\"https://doi.org/10.1017/s0963548322000360\">10.1017/s0963548322000360</a>","short":"D. Conlon, J. Fox, Y. Wigderson, Combinatorics, Probability and Computing 32 (2023) 516–545.","mla":"Conlon, David, et al. “Off-Diagonal Book Ramsey Numbers.” <i>Combinatorics, Probability and Computing</i>, vol. 32, no. 3, Cambridge University Press, 2023, pp. 516–45, doi:<a href=\"https://doi.org/10.1017/s0963548322000360\">10.1017/s0963548322000360</a>.","chicago":"Conlon, David, Jacob Fox, and Yuval Wigderson. “Off-Diagonal Book Ramsey Numbers.” <i>Combinatorics, Probability and Computing</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/s0963548322000360\">https://doi.org/10.1017/s0963548322000360</a>.","apa":"Conlon, D., Fox, J., &#38; Wigderson, Y. (2023). Off-diagonal book Ramsey numbers. <i>Combinatorics, Probability and Computing</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0963548322000360\">https://doi.org/10.1017/s0963548322000360</a>"},"date_published":"2023-05-01T00:00:00Z","month":"05","extern":"1","publisher":"Cambridge University Press","intvolume":"        32","publication":"Combinatorics, Probability and Computing","date_created":"2026-06-29T10:53:47Z","year":"2023","publication_status":"published","date_updated":"2026-07-14T08:27:40Z","scopus_import":"1","OA_type":"green","author":[{"full_name":"Conlon, David","first_name":"David","last_name":"Conlon"},{"full_name":"Fox, Jacob","last_name":"Fox","first_name":"Jacob"},{"first_name":"Yuval","last_name":"Wigderson","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval"}],"abstract":[{"text":"The book graph 𝐵(𝑘)\r\n𝑛 consists of 𝑛 copies of 𝐾𝑘+1 joined along a common 𝐾𝑘. In the prequel to this paper, we studied the diagonal Ramsey number 𝑟⁡(𝐵(𝑘)\r\n𝑛,𝐵(𝑘)\r\n𝑛). Here we consider the natural off-diagonal variant 𝑟⁡(𝐵(𝑘)\r\n𝑐⁢𝑛,𝐵(𝑘)\r\n𝑛) for fixed 𝑐 ∈(0,1]. In this more general setting, we show that an interesting dichotomy emerges: for very small 𝑐, a simple 𝑘-partite construction dictates the Ramsey function and all nearly-extremal colourings are close to being 𝑘-partite, while, for 𝑐 bounded away from 0, random colourings of an appropriate density are asymptotically optimal and all nearly-extremal colourings are quasirandom. Our investigations also open up a range of questions about what happens for intermediate values of 𝑐.\r\n\r\n","lang":"eng"}],"language":[{"iso":"eng"}],"type":"journal_article","OA_place":"repository","quality_controlled":"1","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2110.14483"}],"volume":32,"article_processing_charge":"No","article_type":"original","external_id":{"arxiv":["2110.14483"]},"issue":"3","keyword":["Ramsey theory","book graphs","Ramsey goodness"],"oa":1,"doi":"10.1017/s0963548322000360","mathsc":["05C55","05D10"],"fulldoi":"https://doi.org/10.1017/s0963548322000360","arxiv":1,"page":"516-545","publication_identifier":{"eissn":["1469-2163"],"issn":["0963-5483"]},"day":"01","title":"Off-diagonal book Ramsey numbers","_id":"22165","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"month":"11","extern":"1","publisher":"Cambridge University Press","date_published":"2016-11-01T00:00:00Z","citation":{"ieee":"M. Krivelevich, M. A. Kwan, and B. Sudakov, “Cycles and matchings in randomly perturbed digraphs and hypergraphs,” <i>Combinatorics, Probability and Computing</i>, vol. 25, no. 6. Cambridge University Press, pp. 909–927, 2016.","ista":"Krivelevich M, Kwan MA, Sudakov B. 2016. Cycles and matchings in randomly perturbed digraphs and hypergraphs. Combinatorics, Probability and Computing. 25(6), 909–927.","ama":"Krivelevich M, Kwan MA, Sudakov B. Cycles and matchings in randomly perturbed digraphs and hypergraphs. <i>Combinatorics, Probability and Computing</i>. 2016;25(6):909-927. doi:<a href=\"https://doi.org/10.1017/s0963548316000079\">10.1017/s0963548316000079</a>","short":"M. Krivelevich, M.A. Kwan, B. Sudakov, Combinatorics, Probability and Computing 25 (2016) 909–927.","mla":"Krivelevich, Michael, et al. “Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs.” <i>Combinatorics, Probability and Computing</i>, vol. 25, no. 6, Cambridge University Press, 2016, pp. 909–27, doi:<a href=\"https://doi.org/10.1017/s0963548316000079\">10.1017/s0963548316000079</a>.","chicago":"Krivelevich, Michael, Matthew Alan Kwan, and Benny Sudakov. “Cycles and Matchings in Randomly Perturbed Digraphs and Hypergraphs.” <i>Combinatorics, Probability and Computing</i>. Cambridge University Press, 2016. <a href=\"https://doi.org/10.1017/s0963548316000079\">https://doi.org/10.1017/s0963548316000079</a>.","apa":"Krivelevich, M., Kwan, M. A., &#38; Sudakov, B. (2016). Cycles and matchings in randomly perturbed digraphs and hypergraphs. <i>Combinatorics, Probability and Computing</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0963548316000079\">https://doi.org/10.1017/s0963548316000079</a>"},"oa_version":"Preprint","publication":"Combinatorics, Probability and Computing","year":"2016","date_created":"2021-06-22T12:35:13Z","publication_status":"published","intvolume":"        25","author":[{"first_name":"Michael","last_name":"Krivelevich","full_name":"Krivelevich, Michael"},{"orcid":"0000-0002-4003-7567","last_name":"Kwan","first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"full_name":"Sudakov, Benny","last_name":"Sudakov","first_name":"Benny"}],"date_updated":"2023-02-23T14:02:07Z","scopus_import":"1","status":"public","quality_controlled":"1","type":"journal_article","abstract":[{"text":"We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation. First, we prove that adding linearly many random edges to a dense k-uniform hypergraph ensures the (asymptotically almost sure) existence of a perfect matching or a loose Hamilton cycle. The proof involves an interesting application of Szemerédi's Regularity Lemma, which might be independently useful. We next prove that digraphs with certain strong expansion properties are pancyclic, and use this to show that adding a linear number of random edges typically makes a dense digraph pancyclic. Finally, we prove that perturbing a certain (minimum-degree-dependent) number of random edges in a tournament typically ensures the existence of multiple edge-disjoint Hamilton cycles. All our results are tight.","lang":"eng"}],"language":[{"iso":"eng"}],"article_type":"original","external_id":{"arxiv":["1501.04816"]},"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1501.04816"}],"volume":25,"oa":1,"doi":"10.1017/s0963548316000079","issue":"6","arxiv":1,"page":"909-927","publication_identifier":{"issn":["0963-5483"],"eissn":["1469-2163"]},"day":"01","fulldoi":"https://doi.org/10.1017/s0963548316000079","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","_id":"9591","title":"Cycles and matchings in randomly perturbed digraphs and hypergraphs"}]