[{"ddc":["500"],"publisher":"Cambridge University Press","year":"2025","date_published":"2025-01-06T00:00:00Z","page":"1-43","article_processing_charge":"No","_id":"19017","external_id":{"arxiv":["2403.04474"],"isi":["001416788600001"]},"author":[{"full_name":"Glock, Stefan","last_name":"Glock","first_name":"Stefan"},{"full_name":"Kim, Jaehoon","last_name":"Kim","first_name":"Jaehoon"},{"first_name":"Lyuben","last_name":"Lichev","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","full_name":"Lichev, Lyuben"},{"first_name":"Oleg","full_name":"Pikhurko, Oleg","last_name":"Pikhurko"},{"last_name":"Sun","full_name":"Sun, Shumin","first_name":"Shumin"}],"isi":1,"tmp":{"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","image":"/images/cc_by.png"},"citation":{"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.","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>","short":"S. Glock, J. Kim, L. Lichev, O. Pikhurko, S. Sun, Canadian Journal of Mathematics (2025) 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>.","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>.","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."},"status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4153/s0008414x25000021"}],"scopus_import":"1","publication_status":"epub_ahead","department":[{"_id":"MaKw"}],"day":"06","doi":"10.4153/s0008414x25000021","month":"01","language":[{"iso":"eng"}],"quality_controlled":"1","oa_version":"Published Version","arxiv":1,"date_created":"2025-02-10T08:39:46Z","publication":"Canadian Journal of Mathematics","publication_identifier":{"issn":["0008-414X"],"eissn":["1496-4279"]},"abstract":[{"lang":"eng","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."}],"type":"journal_article","date_updated":"2025-09-30T10:28:07Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"On the (k + 2, k)-problem of Brown, Erdős, and Sós for k = 5,6,7","OA_type":"hybrid","article_type":"original","OA_place":"publisher","oa":1,"has_accepted_license":"1"}]