{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T04:58:23Z","timestamp":1698037103716},"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>We present a new condition on the degree sums of a graph that implies the existence of a long cycle. Let c(G)<\/jats:italic> denote the length of a longest cycle in the graph G<\/jats:italic> and let m<\/jats:italic> be any positive integer. Suppose G<\/jats:italic> is a 2\u2010connected graph with vertices x1<\/jats:sub>,\u2026,xn<\/jats:sub> and edge set E<\/jats:italic> that satisfies the property that, for any two integers j<\/jats:italic> and k<\/jats:italic> with j<\/jats:italic> < k, xj<\/jats:sub>xk<\/jats:sub> \u2209 E<\/jats:italic>, d<\/jats:italic>(x<\/jats:italic>i<\/jats:sub>) \u2a7d j and d<\/jats:italic>(xk<\/jats:sub>) \u2a7d K<\/jats:italic> \u2010 1, we have (1) d<\/jats:italic>(xi<\/jats:sub>) + d(xk<\/jats:sub> \u2a7e m<\/jats:italic> if j<\/jats:italic> + k<\/jats:italic> \u2a7e n<\/jats:italic> and (2) if j<\/jats:italic> + k<\/jats:italic> < n<\/jats:italic>, either m<\/jats:italic> \u2a7e n<\/jats:italic> or d<\/jats:italic>(xj<\/jats:sub>) + d<\/jats:italic>(xk<\/jats:sub>) \u2a7e min(K<\/jats:italic> + 1,m<\/jats:italic>). Then c<\/jats:italic>(G<\/jats:italic>) \u2a7e min(m, n<\/jats:italic>). This result unifies previous results of J.C. Bermond and M. Las Vergnas, respectively.<\/jats:p>","DOI":"10.1002\/jgt.3190130308","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:26:39Z","timestamp":1180182399000},"page":"331-334","source":"Crossref","is-referenced-by-count":2,"title":["A degree condition for the circumference of a graph"],"prefix":"10.1002","volume":"13","author":[{"given":"Nathaniel","family":"Dean","sequence":"first","affiliation":[]},{"given":"Pierre","family":"Fraisse","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"41","article-title":"On hamiltonian walks","volume":"15","author":"Bermond J. C.","year":"1975","journal-title":"Congressus Numerantium"},{"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","first-page":"1297","article-title":"Sur une propri\u00e9t\u00e9 des arbres maximaux dans un graphs","volume":"272","author":"Las Vergnas M.","year":"1971","journal-title":"C.R.A.S. Ser. A"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90031-5"},{"key":"e_1_2_1_6_2","volume-title":"Combinatorial Problems and Exercises","author":"Lov\u00e1sz L.","year":"1979"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130308","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:27:59Z","timestamp":1697981279000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130308"}},"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.3190130308"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130308","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]]}}}