{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T02:15:35Z","timestamp":1698286535605},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5513,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1991,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a graph on <jats:italic>n<\/jats:italic> vertices and <jats:italic>N<\/jats:italic><jats:sub>2<\/jats:sub>(<jats:italic>G<\/jats:italic>) denote the minimum size of <jats:italic>N<\/jats:italic>(<jats:italic>u<\/jats:italic>) \u222a <jats:italic>N<\/jats:italic>(<jats:italic>v<\/jats:italic>) taken over all pairs of independent vertices <jats:italic>u, v<\/jats:italic> of <jats:italic>G<\/jats:italic>. We show that if <jats:italic>G<\/jats:italic> is 3\u2010connected and <jats:italic>N<\/jats:italic><jats:sub>2<\/jats:sub>(<jats:italic>G<\/jats:italic>) \u2a7e \u00bd(<jats:italic>n<\/jats:italic> + 1), then <jats:italic>G<\/jats:italic> has a Hamilton cycle. We show further that if <jats:italic>G<\/jats:italic> is 2\u2010connected and <jats:italic>N<\/jats:italic><jats:sub>2<\/jats:sub>(<jats:italic>G<\/jats:italic>) \u2a7e \u00bd(<jats:italic>n<\/jats:italic> + 3), then either <jats:italic>G<\/jats:italic> has a Hamilton cycle or else <jats:italic>G<\/jats:italic> belongs to one of three families of exceptional graphs.<\/jats:p>","DOI":"10.1002\/jgt.3190150409","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:51:35Z","timestamp":1181285495000},"page":"443-451","source":"Crossref","is-referenced-by-count":13,"title":["Neighborhood unions and hamilton cycles"],"prefix":"10.1002","volume":"15","author":[{"given":"Bill","family":"Jackson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"H. J.Broesma J.Van den Heuvel andH. J.Veldman A generalization of Ore's theorem involving neighborhood unions. University of Twente preprint."},{"key":"e_1_2_1_3_2","unstructured":"R. J.Faudree R. J.Gould M. S.Jacobson andL.Lesniak Neighborhood unions and a generalization of Dirac's Theorem. Preprint."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(89)90060-9"},{"key":"e_1_2_1_5_2","unstructured":"R. J.GouldandM. S.Jacobson Neighborhood intersections and a generalizations of Ore's Theorem.Proceedings of the 2nd International Conference on Graph Theory San Francisco(1989) to appear."},{"key":"e_1_2_1_6_2","article-title":"The effects of distance and neighborhood union conditions on Hamiltonian properties in graphs","author":"Lindquester T.","journal-title":"J. Graph Theory"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2308928"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.3138\/9781487584863"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1967-121-2"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190150409","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190150409","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T03:46:54Z","timestamp":1698032814000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190150409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1991,9]]}},"alternative-id":["10.1002\/jgt.3190150409"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190150409","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}