{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:35:27Z","timestamp":1774528527004,"version":"3.50.1"},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4176,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> = <jats:italic>G(A, B)<\/jats:italic> be a bipartite graph with |A| = <jats:italic>u<\/jats:italic>, |B| = <jats:italic>v<\/jats:italic>, and let \/ be a positive integer. In this paper we prove the following result: If <jats:italic>v<\/jats:italic> \u2264 <jats:italic>u<\/jats:italic>, <jats:italic>uv<\/jats:italic> \u2264 <jats:italic>n, m<\/jats:italic> = |<jats:italic>E(G)<\/jats:italic>|, and <jats:italic>m<\/jats:italic> \u2265 max{180\/<jats:italic>u<\/jats:italic>, 20\/<jats:italic>n<\/jats:italic><jats:sup>1\/2(1+(1\/l))},<\/jats:sup> then <jats:italic>G<\/jats:italic> contains a <jats:italic>C<\/jats:italic><jats:sub>2\/<\/jats:sub>. \u00a9 1995 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190190305","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T13:55:45Z","timestamp":1180187745000},"page":"323-331","source":"Crossref","is-referenced-by-count":16,"title":["Cycles in bipartite graphs and an application in number theory"],"prefix":"10.1002","volume":"19","author":[{"given":"G\u00e1bor","family":"N. S\u00e1rk\u00f6zy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90052-5"},{"key":"e_1_2_1_3_2","unstructured":"D.de CaenandL. A.Sz\u00e9kely The maximum size of 4\u2010 and 6\u2010cycle free bipartite graphs on m n vertices.Coll. Math. Soc. J. Bolyai(1991)."},{"key":"e_1_2_1_4_2","series-title":"Proceedings of the Symposium Smolenice, 1963","first-page":"29","volume-title":"Extremal problems in graph theory","author":"Erd\u00f5s P.","year":"1965"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759702"},{"key":"e_1_2_1_6_2","unstructured":"P.Erd\u00f5s A.S\u00e1rk\u00f6zy andV. T.S\u00f3s On product representions of powers I. Submitted for publication."},{"key":"e_1_2_1_7_2","unstructured":"R.FaudreeandM.Simonovits On a class of degenerate extremal problems II. In prepartion."},{"key":"e_1_2_1_8_2","unstructured":"F.Lazebnik V. A.Ustimenko andA. J.Woldar New constructions of bipartite graphs on m n vertices with many edges and without small cycles. Submitted for publication."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190190305","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190190305","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:58:25Z","timestamp":1698353905000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190190305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,5]]}},"alternative-id":["10.1002\/jgt.3190190305"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190190305","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5]]}}}