{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T05:51:22Z","timestamp":1775022682558,"version":"3.50.1"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"1-2","license":[{"start":{"date-parts":[[2012,2,2]],"date-time":"2012-02-02T00:00:00Z","timestamp":1328140800000},"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":[[2012,3]]},"abstract":"<jats:p>Recently, the authors gave upper bounds for the size of 3-uniform hypergraphs avoiding a given odd cycle using the definition of a cycle due to Berge. In the present paper we extend this bound to <jats:italic>m<\/jats:italic>-uniform hypergraphs (for all <jats:italic>m<\/jats:italic> \u2265 3), as well as <jats:italic>m<\/jats:italic>-uniform hypergraphs avoiding a cycle of length 2<jats:italic>k<\/jats:italic>. Finally we consider non-uniform hypergraphs <jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548311000691_char1\"\/><\/jats:private-char> avoiding cycles of length 2<jats:italic>k<\/jats:italic> or 2<jats:italic>k<\/jats:italic> + 1. In both cases we can bound <jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548311000691_char2\"\/><\/jats:private-char> |<jats:italic>h<\/jats:italic>| by <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>1+1\/<jats:italic>k<\/jats:italic><\/jats:sup>) under the assumption that all <jats:italic>h<\/jats:italic> \u2208 \u03b5(<jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548311000691_char1\"\/><\/jats:private-char>) satisfy |<jats:italic>h<\/jats:italic>| \u2265 4<jats:italic>k<\/jats:italic><jats:sup>2<\/jats:sup>.<\/jats:p>","DOI":"10.1017\/s0963548311000691","type":"journal-article","created":{"date-parts":[[2012,3,19]],"date-time":"2012-03-19T11:20:59Z","timestamp":1332156059000},"page":"193-201","source":"Crossref","is-referenced-by-count":43,"title":["Hypergraphs with No Cycle of a Given Length"],"prefix":"10.1017","volume":"21","author":[{"given":"ERVIN","family":"GY\u0150RI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NATHAN","family":"LEMONS","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,2,2]]},"reference":[{"key":"S0963548311000691_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007108"},{"key":"S0963548311000691_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90052-5"},{"key":"S0963548311000691_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.08.016"},{"key":"S0963548311000691_ref6","unstructured":"[6] Gy\u0151ri E. and Lemons N. 3-uniform hypergraphs avoiding a given odd cycle. Combinatorica, to appear."},{"key":"S0963548311000691_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2005.12.037"},{"key":"S0963548311000691_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.12.004"},{"key":"S0963548311000691_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000691","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T21:25:26Z","timestamp":1556227526000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000691\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,2]]},"references-count":7,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["S0963548311000691"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000691","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,2]]}}}