{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T01:52:30Z","timestamp":1725155550415},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2019,11,27]],"date-time":"2019-11-27T00:00:00Z","timestamp":1574812800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2020,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The maximum size of an <jats:italic>r<\/jats:italic>-uniform hypergraph without a Berge cycle of length at least <jats:italic>k<\/jats:italic> has been determined for all <jats:italic>k<\/jats:italic> \u2265 <jats:italic>r<\/jats:italic> + 3 by F\u00fcredi, Kostochka and Luo and for <jats:italic>k<\/jats:italic> &lt; <jats:italic>r<\/jats:italic> (and <jats:italic>k<\/jats:italic> = <jats:italic>r<\/jats:italic>, asymptotically) by Kostochka and Luo. In this paper we settle the remaining cases: <jats:italic>k<\/jats:italic> = <jats:italic>r<\/jats:italic> + 1 and <jats:italic>k<\/jats:italic> = <jats:italic>r<\/jats:italic> + 2, proving a conjecture of F\u00fcredi, Kostochka and Luo.<\/jats:p>","DOI":"10.1017\/s0963548319000415","type":"journal-article","created":{"date-parts":[[2019,11,27]],"date-time":"2019-11-27T06:58:22Z","timestamp":1574837902000},"page":"423-435","source":"Crossref","is-referenced-by-count":3,"title":["Avoiding long Berge cycles: the missing cases <i>k<\/i> = <i>r<\/i> + 1 and <i>k<\/i> = <i>r<\/i> + 2"],"prefix":"10.1017","volume":"29","author":[{"given":"Beka","family":"Ergemlidze","sequence":"first","affiliation":[]},{"given":"Ervin","family":"Gy\u0151ri","sequence":"additional","affiliation":[]},{"given":"Abhishek","family":"Methuku","sequence":"additional","affiliation":[]},{"given":"Nika","family":"Salia","sequence":"additional","affiliation":[]},{"given":"Casey","family":"Tompkins","sequence":"additional","affiliation":[]},{"given":"Oscar","family":"Zamora","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,11,27]]},"reference":[{"key":"S0963548319000415_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2018.06.006"},{"key":"S0963548319000415_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2019.01.001"},{"key":"S0963548319000415_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2016.05.012"},{"key":"S0963548319000415_ref7","doi-asserted-by":"publisher","DOI":"10.1137\/16M1066191"},{"key":"S0963548319000415_ref4","unstructured":"[4] F\u00fcredi, Z. , Kostochka, A. and Luo, R. (2018) Avoiding long Berge cycles, II: Exact bounds for all n. arXiv:1807.06119"},{"key":"S0963548319000415_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"S0963548319000415_ref11","unstructured":"[11] Kostochka, A. and Luo, R. (2018) On r-uniform hypergraphs with circumference less than r. arXiv:1807.04683"},{"key":"S0963548319000415_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2017.07.003"},{"key":"S0963548319000415_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2018.12.001"},{"key":"S0963548319000415_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2017.10.006"},{"key":"S0963548319000415_ref6","unstructured":"[6] Gerbner, D. , Methuku, A. and Palmer, C. (2018) General lemmas for Berge\u2013Tur\u00e1n hypergraph problems. arXiv:1808.10842"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548319000415","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,26]],"date-time":"2020-05-26T10:27:04Z","timestamp":1590488824000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548319000415\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,27]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["S0963548319000415"],"URL":"https:\/\/doi.org\/10.1017\/s0963548319000415","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,27]]}}}