{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T04:55:13Z","timestamp":1780635313561,"version":"3.54.1"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,12,1]],"date-time":"2014-12-01T00:00:00Z","timestamp":1417392000000},"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":[[2015,7]]},"abstract":"<jats:p>We describe the<jats:italic>C<\/jats:italic><jats:sup>2<jats:italic>k<\/jats:italic>+1<\/jats:sup>-free graphs on<jats:italic>n<\/jats:italic>vertices with maximum number of edges. The extremal graphs are unique for<jats:italic>n<\/jats:italic>\u2209 {3<jats:italic>k<\/jats:italic>\u2212 1, 3<jats:italic>k<\/jats:italic>, 4<jats:italic>k<\/jats:italic>\u2212 2, 4<jats:italic>k<\/jats:italic>\u2212 1}. The value of<jats:italic>ex<\/jats:italic>(<jats:italic>n<\/jats:italic>,<jats:italic>C<\/jats:italic><jats:sub>2<jats:italic>k<\/jats:italic>+1<\/jats:sub>) can be read out from the works of Bondy [3], Woodall [14], and Bollob\u00e1s [1], but here we give a new streamlined proof. The complete determination of the extremal graphs is also new.<\/jats:p><jats:p>We obtain that the bound for<jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub>(<jats:italic>C<\/jats:italic><jats:sub>2<jats:italic>k<\/jats:italic>+1<\/jats:sub>) is 4<jats:italic>k<\/jats:italic>in the classical theorem of Simonovits, from which the unique extremal graph is the bipartite Tur\u00e1n graph.<\/jats:p>","DOI":"10.1017\/s0963548314000601","type":"journal-article","created":{"date-parts":[[2014,12,1]],"date-time":"2014-12-01T11:39:01Z","timestamp":1417433941000},"page":"641-645","source":"Crossref","is-referenced-by-count":46,"title":["Extremal Numbers for Odd Cycles"],"prefix":"10.1017","volume":"24","author":[{"given":"ZOLTAN","family":"F\u00dcREDI","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"DAVID S.","family":"GUNDERSON","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,12,1]]},"reference":[{"key":"S0963548314000601_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(71)90019-7"},{"key":"S0963548314000601_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(75)90080-5"},{"key":"S0963548314000601_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"S0963548314000601_ref13","doi-asserted-by":"publisher","DOI":"10.4064\/cm-3-1-19-30"},{"key":"S0963548314000601_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(97)00032-2"},{"key":"S0963548314000601_ref10","first-page":"60","article-title":"Solution to Problem 28, by H. Gouwentak, W. Mantel, J. Teixeira de Mattes, F. Schuh, and W. A. Wythoff","volume":"10","author":"Mantel","year":"1907","journal-title":"Wiskundige Opgaven"},{"key":"S0963548314000601_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01902497"},{"key":"S0963548314000601_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9967-7"},{"key":"S0963548314000601_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90044-2"},{"key":"S0963548314000601_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(71)90016-5"},{"key":"S0963548314000601_ref8","doi-asserted-by":"crossref","unstructured":"F\u00fcredi Z. and Simonovits M. (2013) The history of degenerate (bipartite) extremal graph problems. In Erd\u0151s Centennial ( L. Lov\u00e1sz et al., eds), Vol. 25 of Bolyai Society Mathematical Studies, pp. 167\u2013262.","DOI":"10.1007\/978-3-642-39286-3_7"},{"key":"S0963548314000601_ref9","first-page":"19","article-title":"Maximal paths and cycles in a graph","volume":"234","author":"Kopylov","year":"1977","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"S0963548314000601_ref12","first-page":"436","article-title":"Eine Extremalaufgabe aus der Graphentheorie (in Hungarian)","volume":"48","author":"Tur\u00e1n","year":"1941","journal-title":"Math. Fiz Lapok"},{"key":"S0963548314000601_ref14","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-24.4.739"},{"key":"S0963548314000601_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-012-1212-9"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548314000601","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,18]],"date-time":"2019-08-18T00:10:16Z","timestamp":1566087016000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548314000601\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,1]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["S0963548314000601"],"URL":"https:\/\/doi.org\/10.1017\/s0963548314000601","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,1]]}}}