{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T13:11:02Z","timestamp":1698066662988},"reference-count":7,"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>Ore proved in 1960 that if G<\/jats:italic> is a graph of order n<\/jats:italic> and the sum of the degrees of any pair of nonadjacent vertices is at least n<\/jats:italic>, then G<\/jats:italic> has a hamiltonian cycle. In 1986, Li Hao and Zhu Yongjin showed that if n<\/jats:italic> \u2a7e 20 and the minimum degree \u03b4 is at least 5, then the graph G<\/jats:italic> above contains at least two edge disjoint hamiltonian cycles. The result of this paper is that if n<\/jats:italic> \u2a7e 2\u03b42<\/jats:sup>, then for any 3 \u2a7d l1<\/jats:sub> \u2a7d l2<\/jats:sub> \u2a7d \u20db \u2a7d lk<\/jats:sub> \u2a7d n<\/jats:italic>, 1 = k = [(\u03b4 \u2010 1)\/2], such graph has K<\/jats:italic> edge disjoint cycles with lengths l1<\/jats:sub>, l2<\/jats:sub>\u2026lk<\/jats:sub>, respectively. In particular, when l1<\/jats:sub> = l2<\/jats:sub> = \u20db = lk<\/jats:sub> = n<\/jats:italic> and k<\/jats:italic> = [(\u03b4 \u2010 1)\/2], the graph contains [(\u03b4 \u2010 1)\/2] edge disjoint hamiltonian cycles.<\/jats:p>","DOI":"10.1002\/jgt.3190130306","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:26:46Z","timestamp":1180182406000},"page":"313-322","source":"Crossref","is-referenced-by-count":5,"title":["Edge disjoint cycles in graphs"],"prefix":"10.1002","volume":"13","author":[{"given":"Li","family":"Hao","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70494-1"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_4_2","first-page":"231","volume-title":"Graph Theory with Applications to Algorithms and Computer Science","author":"Faudree R. J.","year":"1985"},{"key":"e_1_2_1_5_2","unstructured":"L.Hao Hamiltonian cycles and circumferences in graphs. Ph.D. dissertation (1986) Institute of System Science Academia Sinica."},{"key":"e_1_2_1_6_2","unstructured":"L.HaoandZ.Yongjin Edge disjoint hamiltonian cycles submitted."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2308928"},{"key":"e_1_2_1_8_2","first-page":"12","article-title":"The progress of hamilton problems in graph theory","volume":"2","author":"Yongjin Z.","year":"1985","journal-title":"J. Qufu Teachers College"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:28:11Z","timestamp":1697981291000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,7]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,7]]}},"alternative-id":["10.1002\/jgt.3190130306"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130306","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]]}}}