{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:40:35Z","timestamp":1698043235904},"reference-count":5,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6305,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,7]]},"abstract":"Abstract<\/jats:title>The main theorem of that paper is the following: let G<\/jats:italic> be a graph of order n<\/jats:italic>, of size at least (n2<\/jats:sup> \u2010 3n + 6)\/2. For any integers k<\/jats:italic>, n1<\/jats:sub>, n2<\/jats:sub>,\u2026,nk<\/jats:sub> such that n = n1<\/jats:sub> + n2<\/jats:sub> +. + nk<\/jats:sub> and ni<\/jats:sub> \u2a7e 3, there exists a covering of the vertices of G<\/jats:italic> by disjoint cycles (C<\/jats:italic>i<\/jats:sub>) =l\u2026k<\/jats:italic> with |C<\/jats:italic>i<\/jats:sub>| = ni, except when n<\/jats:italic> = 6, n<\/jats:italic>1<\/jats:sub> = 3, n<\/jats:italic>2<\/jats:sub> = 3, and G<\/jats:italic> is isomorphic to G<\/jats:italic>1<\/jats:sub>, the complement of G<\/jats:italic>1<\/jats:sub> consisting of a C<\/jats:italic>3<\/jats:sub> and a stable set of three vertices, or when n<\/jats:italic> = 9, n<\/jats:italic>1<\/jats:sub> = n<\/jats:italic>2<\/jats:sub> = n<\/jats:italic>3<\/jats:sub> = 3, and G<\/jats:italic> is isomorphic to G<\/jats:italic>2<\/jats:sub>, the complement of G<\/jats:italic>2<\/jats:sub> consisting of a complete graph on four vertices and a stable set of five vertices.<\/jats:p>We prove an analogous theorem for bipartite graphs: let G<\/jats:italic> be a bipartite balanced graph of order 2n<\/jats:italic>, of size at least n2<\/jats:sup> \u2010 n + 2. For any integers s, n1<\/jats:sub>, n2<\/jats:sub>,\u2026,ns<\/jats:sub><\/jats:italic> with n<\/jats:italic>i<\/jats:sub> \u2a7e 2 and n<\/jats:italic> = n<\/jats:italic>1<\/jats:sub> + n<\/jats:italic>2<\/jats:sub> + \u20db + n<\/jats:italic>s<\/jats:sub>, there exists a covering of the vertices of G<\/jats:italic> by s<\/jats:italic> disjoint cycles C<\/jats:italic>i<\/jats:sub>, with |C<\/jats:italic>i<\/jats:sub>| = 2n<\/jats:italic>i<\/jats:sub>.<\/jats:p>","DOI":"10.1002\/jgt.3190130307","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:26:42Z","timestamp":1180182402000},"page":"323-330","source":"Crossref","is-referenced-by-count":1,"title":["Covering the vertices of a graph by cycles of prescribed length"],"prefix":"10.1002","volume":"13","author":[{"given":"D.","family":"Amar","sequence":"first","affiliation":[]},{"given":"I.","family":"Fournier","sequence":"additional","affiliation":[]},{"given":"A.","family":"Germa","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01895727"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90050-5"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759704"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02412090"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130307","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:28:12Z","timestamp":1697981292000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,7]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,7]]}},"alternative-id":["10.1002\/jgt.3190130307"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130307","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,7]]}}}