[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Off-diagonal Ramsey numbers for linear hypergraphs","_id":"22152","page":"1-14","publication_identifier":{"eissn":["1469-2163"],"issn":["0963-5483"]},"day":"14","arxiv":1,"fulldoi":"https://doi.org/10.1017/s0963548326100443","oa":1,"doi":"10.1017/s0963548326100443","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"],"article_processing_charge":"No","external_id":{"arxiv":["2507.05641"]},"article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/S0963548326100443"}],"status":"public","quality_controlled":"1","abstract":[{"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).","lang":"eng"}],"language":[{"iso":"eng"}],"type":"journal_article","OA_place":"publisher","author":[{"first_name":"Xiaoyu","last_name":"He","full_name":"He, Xiaoyu"},{"last_name":"Nie","first_name":"Jiaxi","full_name":"Nie, Jiaxi"},{"first_name":"Yuval","last_name":"Wigderson","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval"},{"first_name":"Hung-Hsun","last_name":"Yu","full_name":"Yu, Hung-Hsun"}],"date_updated":"2026-07-08T07:24:54Z","scopus_import":"1","OA_type":"hybrid","year":"2026","date_created":"2026-06-29T10:47:02Z","publication":"Combinatorics, Probability and Computing","publication_status":"epub_ahead","date_published":"2026-04-14T00:00:00Z","extern":"1","month":"04","ddc":["500"],"publisher":"Cambridge University Press","oa_version":"Published Version","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>","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>.","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>.","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."}},{"das_tickbox":"0","article_type":"original","article_processing_charge":"Yes (via OA deal)","volume":58,"has_accepted_license":"1","researchdata_availability":"no","mathsc":["05D40","52C10","52C35"],"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)"},"file":[{"relation":"main_file","date_updated":"2026-10-14T08:37:16Z","success":1,"access_level":"open_access","checksum":"cce830e3fc66174803b91103f5b88a29","creator":"dernst","file_size":284851,"file_name":"2026_BulletinLondonMathSoc_Grebennikov.pdf","date_created":"2026-10-14T08:37:16Z","file_id":"23139","content_type":"application/pdf"}],"project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics","grant_number":"101076777"}],"oa":1,"doi":"10.1112/blms.70510","issue":"10","corr_author":"1","day":"01","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"department":[{"_id":"MaKw"},{"_id":"GradSch"}],"supplementarymaterial":"no","fulldoi":"https://doi.org/10.1112/blms.70510","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"23123","title":"No‐(k+1)‐in‐line problem for large constant k","publisher":"Wiley","month":"10","ddc":["510"],"date_published":"2026-10-01T00:00:00Z","citation":{"ieee":"A. Grebennikov and M. A. Kwan, “No‐(k+1)‐in‐line problem for large constant k,” <i>Bulletin of the London Mathematical Society</i>, vol. 58, no. 10. Wiley, 2026.","ista":"Grebennikov A, Kwan MA. 2026. No‐(k+1)‐in‐line problem for large constant k. Bulletin of the London Mathematical Society. 58(10), e70510.","ama":"Grebennikov A, Kwan MA. No‐(k+1)‐in‐line problem for large constant k. <i>Bulletin of the London Mathematical Society</i>. 2026;58(10). doi:<a href=\"https://doi.org/10.1112/blms.70510\">10.1112/blms.70510</a>","mla":"Grebennikov, Aleksandr, and Matthew Alan Kwan. “No‐(K+1)‐in‐line Problem for Large Constant K.” <i>Bulletin of the London Mathematical Society</i>, vol. 58, no. 10, e70510, Wiley, 2026, doi:<a href=\"https://doi.org/10.1112/blms.70510\">10.1112/blms.70510</a>.","chicago":"Grebennikov, Aleksandr, and Matthew Alan Kwan. “No‐(K+1)‐in‐line Problem for Large Constant K.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2026. <a href=\"https://doi.org/10.1112/blms.70510\">https://doi.org/10.1112/blms.70510</a>.","apa":"Grebennikov, A., &#38; Kwan, M. A. (2026). No‐(k+1)‐in‐line problem for large constant k. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.70510\">https://doi.org/10.1112/blms.70510</a>","short":"A. Grebennikov, M.A. Kwan, Bulletin of the London Mathematical Society 58 (2026)."},"oa_version":"Published Version","publication_status":"published","publication":"Bulletin of the London Mathematical Society","year":"2026","date_created":"2026-10-12T13:57:47Z","intvolume":"        58","acknowledgement":"We would like to thank Huy Pham for insightful discussions about the proof approach, and wewould like to thank the anonymous referees for their careful reading and helpful comments. Bothauthors are supported by ERC Starting Grant “RANDSTRUCT” No. 101076777.Open Access funding provided by Institute of Science and Technology Austria.","article_number":"e70510","file_date_updated":"2026-10-14T08:37:16Z","author":[{"last_name":"Grebennikov","first_name":"Aleksandr","full_name":"Grebennikov, Aleksandr","id":"776468ec-50b0-11ef-861e-96ad19e894f3"},{"orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","last_name":"Kwan"}],"scopus_import":"1","OA_type":"hybrid","date_updated":"2026-10-14T08:41:00Z","quality_controlled":"1","status":"public","PlanS_conform":"1","OA_place":"publisher","type":"journal_article","language":[{"iso":"eng"}],"abstract":[{"text":"How many points can be placed in an 𝑛 × 𝑛 grid sothat every (affine) line contains at most 𝑘 points? Weprove that for 𝑛 ⩾ 𝑘 ⩾ 1037 the maximum number ofpoints is exactly 𝑘𝑛. Our proof builds on the recent workof Kovács, Nagy and Szabó (who proved an analogousresult when 𝑘 is at least about √𝑛 log 𝑛), incorporat-ing ideas of Jain and Pham. Using the same approach,we also obtain new bounds for higher-dimensionalextensions of this problem","lang":"eng"}]}]