{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T09:10:20Z","timestamp":1746522620835},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T00:00:00Z","timestamp":1522627200000},"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":[[2018,9]]},"abstract":"<jats:p>It follows from known results that every regular tripartite hypergraph of positive degree, with <jats:italic>n<\/jats:italic> vertices in each class, has matching number at least <jats:italic>n<\/jats:italic>\/2. This bound is best possible, and the extremal configuration is unique. Here we prove a stability version of this statement, establishing that every regular tripartite hypergraph with matching number at most (1 + \u03f5)<jats:italic>n<\/jats:italic>\/2 is close in structure to the extremal configuration, where \u2018closeness\u2019 is measured by an explicit function of \u03f5.<\/jats:p>","DOI":"10.1017\/s0963548318000147","type":"journal-article","created":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T03:55:23Z","timestamp":1522641323000},"page":"774-793","source":"Crossref","is-referenced-by-count":3,"title":["A Stability Theorem for Matchings in Tripartite 3-Graphs"],"prefix":"10.1017","volume":"27","author":[{"given":"PENNY","family":"HAXELL","sequence":"first","affiliation":[]},{"given":"LOTHAR","family":"NARINS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,4,2]]},"reference":[{"key":"S0963548318000147_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-007-2086-y"},{"key":"S0963548318000147_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/1970012"},{"key":"S0963548318000147_ref8","doi-asserted-by":"crossref","unstructured":"Haxell P. , Narins L. and Szab\u00f3 T. Extremal hypergraphs for Ryser's conjecture. J. Combin. Theory Ser. A, to appear","DOI":"10.1016\/j.jcta.2018.04.004"},{"key":"S0963548318000147_ref11","unstructured":"Narins L. (2014) Extremal hypergraphs for Ryser's conjecture. PhD thesis, Freie Universit\u00e4t Berlin."},{"key":"S0963548318000147_ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-06-03833-5"},{"key":"S0963548318000147_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s004930170001"},{"key":"S0963548318000147_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.06.010"},{"key":"S0963548318000147_ref3","unstructured":"Aharoni R. , Alon N. , Amir M. , Haxell P. , Hefetz D. , Jiang Z. , Kronenberg G. and Naor A. (2017) Ramsey-nice families of graphs. arXiv:1708.07369"},{"key":"S0963548318000147_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02940617"},{"key":"S0963548318000147_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-3165(03)00045-1"},{"key":"S0963548318000147_ref7","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.2728"},{"key":"S0963548318000147_ref12","unstructured":"Ryser H. (1967) Neuere Probleme der Kombinatorik. In Vortr\u00e4ge \u00fcber Kombinatorik Oberwolfach, Mathematisches Forschungsinstitut Oberwolfach, Colloquia Mathematica Societatis J\u00e1nos Bolyai, pp. 69\u201391."},{"key":"S0963548318000147_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0118(200010)35:2<83::AID-JGT2>3.0.CO;2-V"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548318000147","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T16:49:58Z","timestamp":1555174198000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548318000147\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,2]]},"references-count":13,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["S0963548318000147"],"URL":"https:\/\/doi.org\/10.1017\/s0963548318000147","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,2]]}}}