{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T11:47:06Z","timestamp":1775130426068,"version":"3.50.1"},"reference-count":11,"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>In 1965 Erd\u0151s conjectured a formula for the maximum number of edges in a <jats:italic>k<\/jats:italic>-uniform <jats:italic>n<\/jats:italic>-vertex hypergraph without a matching of size <jats:italic>s<\/jats:italic>. We prove this conjecture for <jats:italic>k<\/jats:italic> = 3 and all <jats:italic>s<\/jats:italic> \u2265 1 and <jats:italic>n<\/jats:italic> \u2265 4<jats:italic>s<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0963548311000496","type":"journal-article","created":{"date-parts":[[2012,3,19]],"date-time":"2012-03-19T15:20:59Z","timestamp":1332170459000},"page":"141-148","source":"Crossref","is-referenced-by-count":29,"title":["On the Maximum Number of Edges in a Triple System Not Containing a Disjoint Family of a Given Size"],"prefix":"10.1017","volume":"21","author":[{"given":"PETER","family":"FRANKL","sequence":"first","affiliation":[]},{"given":"VOJTECH","family":"R\u00d6DL","sequence":"additional","affiliation":[]},{"given":"ANDRZEJ","family":"RUCI\u0143SKI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,2,2]]},"reference":[{"key":"S0963548311000496_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"S0963548311000496_ref7","unstructured":"[7] Huang H. , Loh P. and Sudakov B. The size of a hypergraph and its matching number. Submitted."},{"key":"S0963548311000496_ref3","first-page":"93","article-title":"A problem on independent r-tuples","volume":"8","author":"Erd\u0151s","year":"1965","journal-title":"Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math."},{"key":"S0963548311000496_ref5","first-page":"81","volume-title":"Surveys in Combinatorics","author":"Frankl","year":"1987"},{"key":"S0963548311000496_ref9","unstructured":"[9] Lo A. and Markstr\u00f6m K. F-factors in hypergraphs via absorption. Submitted."},{"key":"S0963548311000496_ref2","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/27.1.25"},{"key":"S0963548311000496_ref6","unstructured":"[6] Frankl P. and F\u00fcredi Z. Unpublished."},{"key":"S0963548311000496_ref1","unstructured":"[1] Alon N. , Frankl P. , Huang H. , R\u00f6dl V. , Ruci\u0144ski A. and Sudakov B. On the existence of large matchings and fractional matchings in uniform hypergraphs. Submitted."},{"key":"S0963548311000496_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2011.02.001"},{"key":"S0963548311000496_ref11","doi-asserted-by":"crossref","unstructured":"[11] R\u00f6dl V. and Ruci\u0144ski A. (2010) Dirac-type questions for hypergraphs: A survey (or more problems for Endre to solve). In An Irregular Mind: Szemer\u00e9di is 70, Vol. 21 of Bolyai Soc. Math. Studies, pp. 561\u2013590.","DOI":"10.1007\/978-3-642-14444-8_16"},{"key":"S0963548311000496_ref8","unstructured":"[8] Khan I. Perfect matchings in 4-uniform hypergraphs. Submitted."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000496","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T01:24:55Z","timestamp":1556241895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000496\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,2]]},"references-count":11,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["S0963548311000496"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000496","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]]}}}