{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T02:46:39Z","timestamp":1764557199164},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,7,2]],"date-time":"2010-07-02T00:00:00Z","timestamp":1278028800000},"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":[[2011,1]]},"abstract":"<jats:p>The asymptotics of 2-colour Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs were recently determined [16, 17]. We address the same problem for Berge cycles and for 3 colours. Our main result is that the 3-colour Ramsey number of a 3-uniform Berge cycle of length <jats:italic>n<\/jats:italic> is asymptotic to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548310000209_inline1\"><jats:alt-text>$\\frac{5n}{4}$<\/jats:alt-text><\/jats:inline-graphic>. The result is proved with the Regularity Lemma via the existence of a monochromatic connected matching covering asymptotically 4<jats:italic>n<\/jats:italic>\/5 vertices in the multicoloured 2-shadow graph induced by the colouring of <jats:italic>K<jats:sub>n<\/jats:sub><\/jats:italic><jats:sup>(3)<\/jats:sup>.<\/jats:p>","DOI":"10.1017\/s0963548310000209","type":"journal-article","created":{"date-parts":[[2010,7,2]],"date-time":"2010-07-02T12:01:24Z","timestamp":1278072084000},"page":"53-71","source":"Crossref","is-referenced-by-count":7,"title":["The 3-Colour Ramsey Number of a 3-Uniform Berge Cycle"],"prefix":"10.1017","volume":"20","author":[{"given":"ANDR\u00c1S","family":"GY\u00c1RF\u00c1S","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00c1BOR N.","family":"S\u00c1RK\u00d6ZY","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,7,2]]},"reference":[{"key":"S0963548310000209_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.11.006"},{"key":"S0963548310000209_ref29","first-page":"399","volume-title":"Probl\u00e8mes Combinatoires et Th\u00e1orie des Graphes","author":"Szemer\u00e1di","year":"1978"},{"key":"S0963548310000209_ref28","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20017"},{"key":"S0963548310000209_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90035-X"},{"key":"S0963548310000209_ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007042"},{"key":"S0963548310000209_ref24","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1998.1874"},{"key":"S0963548310000209_ref22","unstructured":"[22] Koml\u00f3s J. and Simonovits M. (1996) Szemer\u00e1di's Regularity Lemma and its applications in graph theory. In Combinatorics: Paul Erd\u0151s is Eighty ( Mikl\u00f3s D. , S\u00f3s V. T. , and Sz\u0151nyi T. , eds), Vol. 2 of Bolyai Society Math. Studies, pp. 295\u2013352."},{"key":"S0963548310000209_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01196135"},{"key":"S0963548310000209_ref19","unstructured":"[19] Kohayakawa Y. , Simonovits M. and Skokan J. The 3-color Ramsey number of odd cycles. Manuscript. J. Combin. Theory Ser. B, to appear."},{"key":"S0963548310000209_ref18","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199903)30:3<205::AID-JGT5>3.0.CO;2-O"},{"key":"S0963548310000209_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S096354830800967X"},{"key":"S0963548310000209_ref15","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20231"},{"key":"S0963548310000209_ref23","volume-title":"Matching Theory","author":"Lov\u00e1sz","year":"1986"},{"key":"S0963548310000209_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-33700-8_8"},{"key":"S0963548310000209_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-007-0043-4"},{"key":"S0963548310000209_ref2","first-page":"39","volume-title":"Probl\u00e8mes Combinatoires et Th\u00e1orie des Graphes","author":"Bermond","year":"1978"},{"key":"S0963548310000209_ref21","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199805)12:3<297::AID-RSA5>3.0.CO;2-Q"},{"key":"S0963548310000209_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"S0963548310000209_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90036-1"},{"key":"S0963548310000209_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240020208"},{"key":"S0963548310000209_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02351586"},{"key":"S0963548310000209_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.02.007"},{"key":"S0963548310000209_ref8","first-page":"167","article-title":"On Ramsey-type problems","volume":"10","author":"Gerencs\u00e1r","year":"1967","journal-title":"Ann. Univ. Sci. Budapest E\u00f6tv\u00f6s, Sect. Math."},{"key":"S0963548310000209_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.02.005"},{"key":"S0963548310000209_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2007.07.002"},{"key":"S0963548310000209_ref1","volume-title":"Graphs and Hypergraphs","author":"Berge","year":"1973"},{"key":"S0963548310000209_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.09.001"},{"key":"S0963548310000209_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(13)80099-6"},{"key":"S0963548310000209_ref9","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2007.166.897"},{"key":"S0963548310000209_ref10","unstructured":"[10] Gy\u00e1rf\u00e1s A. (1973) Partition coverings and blocking sets of hypergraphs (in Hungarian). Studies of Computer and Automation Research Institute, No. 71, MR0357172."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548310000209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T19:57:07Z","timestamp":1556395027000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548310000209\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,2]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["S0963548310000209"],"URL":"https:\/\/doi.org\/10.1017\/s0963548310000209","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,2]]}}}