{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T08:21:34Z","timestamp":1648974094393},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2012,10,19]],"date-time":"2012-10-19T00:00:00Z","timestamp":1350604800000},"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":[[2013,1]]},"abstract":"<jats:p>A 3-graph is said to contain a generalized 4-cycle if it contains 4 edges <jats:italic>A, B, C, D<\/jats:italic> such that <jats:italic>A<\/jats:italic> \u2229 <jats:italic>B<\/jats:italic>=<jats:italic>C<\/jats:italic> \u2229 <jats:italic>D<\/jats:italic> =\u2205 and <jats:italic>A<\/jats:italic> \u222a <jats:italic>B<\/jats:italic>=<jats:italic>C<\/jats:italic> \u222a <jats:italic>D<\/jats:italic>. We show that a 3-graph in which every pair of vertices is contained in at least 4 edges must contain a generalized 4-cycle. When the number of vertices, <jats:italic>n<\/jats:italic>, is equivalent to 1 or 5 modulo 20, this result is optimum, in the sense that for such <jats:italic>n<\/jats:italic> there are 3-graphs where every pair of vertices is contained in 3 edges but which do not contain a generalized 4-cycle.<\/jats:p>","DOI":"10.1017\/s0963548312000430","type":"journal-article","created":{"date-parts":[[2012,10,19]],"date-time":"2012-10-19T12:59:45Z","timestamp":1350651585000},"page":"112-117","source":"Crossref","is-referenced-by-count":0,"title":["The Largest Minimum Codegree of a 3-Graph Without a Generalized 4-Cycle"],"prefix":"10.1017","volume":"22","author":[{"given":"EDWARD","family":"MARCHANT","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,10,19]]},"reference":[{"key":"S0963548312000430_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579216"},{"key":"S0963548312000430_ref6","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177700182"},{"key":"S0963548312000430_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177705047"},{"key":"S0963548312000430_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548301005028"},{"key":"S0963548312000430_ref2","first-page":"215","article-title":"On a problem of graph theory.","volume":"1","author":"Erd\u0151s","year":"1966","journal-title":"Studia Sci. Math. Hungar"},{"key":"S0963548312000430_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(83)90018-7"},{"key":"S0963548312000430_ref1","first-page":"3","article-title":"Problems and results in combinatorial analysis","volume":"19","author":"Erd\u0151s","year":"1977","journal-title":"Proc. Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing, Congress. Numer."},{"key":"S0963548312000430_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2008.09.002"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548312000430","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T20:06:12Z","timestamp":1556136372000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548312000430\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,19]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["S0963548312000430"],"URL":"https:\/\/doi.org\/10.1017\/s0963548312000430","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,19]]}}}