{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T11:07:23Z","timestamp":1772363243707,"version":"3.50.1"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"1-2","license":[{"start":{"date-parts":[[2009,3,1]],"date-time":"2009-03-01T00:00:00Z","timestamp":1235865600000},"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":[[2009,3]]},"abstract":"<jats:p>Let<jats:italic>C<\/jats:italic><jats:sup>(3)<\/jats:sup><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>denote the 3-uniform<jats:italic>tight cycle<\/jats:italic>, that is, the hypergraph with vertices<jats:italic>v<\/jats:italic><jats:sub>1<\/jats:sub>, .\u2013.\u2013.,<jats:italic>v<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>and edges<jats:italic>v<\/jats:italic><jats:sub>1<\/jats:sub><jats:italic>v<\/jats:italic><jats:sub>2<\/jats:sub><jats:italic>v<\/jats:italic><jats:sub>3<\/jats:sub>,<jats:italic>v<\/jats:italic><jats:sub>2<\/jats:sub><jats:italic>v<\/jats:italic><jats:sub>3<\/jats:sub><jats:italic>v<\/jats:italic><jats:sub>4<\/jats:sub>, .\u2013.\u2013.,<jats:italic>v<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic>\u22121<\/jats:sub><jats:italic>v<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub><jats:italic>v<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>v<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub><jats:italic>v<\/jats:italic><jats:sub>1<\/jats:sub><jats:italic>v<\/jats:italic><jats:sub>2<\/jats:sub>. We prove that the smallest integer<jats:italic>N<\/jats:italic>=<jats:italic>N<\/jats:italic>(<jats:italic>n<\/jats:italic>) for which every red\u2013blue colouring of the edges of the complete 3-uniform hypergraph with<jats:italic>N<\/jats:italic>vertices contains a monochromatic copy of<jats:italic>C<\/jats:italic><jats:sup>(3)<\/jats:sup><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>is asymptotically equal to 4<jats:italic>n<\/jats:italic>\/3 if<jats:italic>n<\/jats:italic>is divisible by 3, and 2<jats:italic>n<\/jats:italic>otherwise. The proof uses the regularity lemma for hypergraphs of Frankl and R\u00f6dl.<\/jats:p>","DOI":"10.1017\/s096354830800967x","type":"journal-article","created":{"date-parts":[[2009,2,4]],"date-time":"2009-02-04T09:28:04Z","timestamp":1233739684000},"page":"165-203","source":"Crossref","is-referenced-by-count":23,"title":["The Ramsey Number for 3-Uniform Tight Hypergraph Cycles"],"prefix":"10.1017","volume":"18","author":[{"given":"P. E.","family":"HAXELL","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"\u0141UCZAK","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"PENG","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"R\u00d6DL","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"RUCI\u0143SKI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"SKOKAN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,1]]},"reference":[{"key":"S096354830800967X_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.09.001"},{"key":"S096354830800967X_ref16","unstructured":"[16] Radziszowski S. P. (1994) Small Ramsey numbers. Electronic J. Combin. 1, Dynamic Survey 1, 30 pp."},{"key":"S096354830800967X_ref8","doi-asserted-by":"crossref","DOI":"10.37236\/850","article-title":"The Ramsey number of diamond-matchings and loose cycles in hypergraphs","volume":"15","author":"Gy\u00e1rf\u00e1s","year":"2008","journal-title":"Electron. J. Combin."},{"key":"S096354830800967X_ref4","unstructured":"[4] Cooley O. , Fountoulakis N. , K\u00fchn D. and Osthus D. Embeddings and Ramsey numbers of sparse k-uniform hypergraphs. Combinatorica, to appear."},{"key":"S096354830800967X_ref19","unstructured":"[19] Szemer\u00e9di E. (1978) Regular partitions of graphs. In Probl\u00e8mes Combinatoires et Th\u00e9orie des Graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976), Vol. 260 of Colloq. Internat. CNRS, CNRS, Paris, pp. 399\u2013401."},{"key":"S096354830800967X_ref12","unstructured":"[12] Haxell P. , \u0141uczak T. , Peng Y. , R\u00f6dl V. , Ruci\u0144ski A. and Skokan J. (2007) The Ramsey number for hypergraph cycles II. CDAM Research Report LSE-CDAM-2007-04."},{"key":"S096354830800967X_ref10","unstructured":"[10] Gy\u00e1rf\u00e1s A. , S\u00e1rk\u00f6zy G. and Szemer\u00e9di E. Monochromatic Hamiltonian 3-tight Berge cycles in 2-colored 4-uniform hypergraphs. Submitted."},{"key":"S096354830800967X_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.02.005"},{"key":"S096354830800967X_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007042"},{"key":"S096354830800967X_ref9","unstructured":"[9] Gy\u00e1rf\u00e1s A. , S\u00e1rk\u00f6zy G. and Szemer\u00e9di E. Long monochromatic Berge cycles in colored 4-uniform hypergraphs. Submitted."},{"key":"S096354830800967X_ref2","doi-asserted-by":"crossref","unstructured":"[2] Conlon D. , Fox J. and Sudakov B. Ramsey numbers of sparse hypergraphs. Random Struct. Algorithms, to appear.","DOI":"10.1002\/rsa.20260"},{"key":"S096354830800967X_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-008-0784-x"},{"key":"S096354830800967X_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10017"},{"key":"S096354830800967X_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(73)80005-X"},{"key":"S096354830800967X_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90151-4"},{"key":"S096354830800967X_ref13","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1998.1874"},{"key":"S096354830800967X_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2007.08.008"},{"key":"S096354830800967X_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2005.12.002"},{"key":"S096354830800967X_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90035-X"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354830800967X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T09:45:46Z","timestamp":1589535946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354830800967X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3]]},"references-count":19,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2009,3]]}},"alternative-id":["S096354830800967X"],"URL":"https:\/\/doi.org\/10.1017\/s096354830800967x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3]]}}}