{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T03:08:15Z","timestamp":1719803295031},"reference-count":5,"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>We consider a generalized degree condition based on the cardinality of the neighborhood union of arbitrary sets of <jats:italic>r<\/jats:italic> vertices. We show that a Dirac\u2010type bound on this degree in conjunction with a bound on the independence number of a graph is sufficient to imply certain hamiltonian properties in graphs. For <jats:italic>K<\/jats:italic><jats:sub>1,m<\/jats:sub>\u2010free grphs we obtain generalizations of known results. In particular we show:<\/jats:p><jats:p>Theorem. Let <jats:italic>r<\/jats:italic> \u2265 1 and <jats:italic>m<\/jats:italic> \u2265 3 be integers. Then for each nonnegative function <jats:italic>f(r, m)<\/jats:italic> there exists a constant <jats:italic>C<\/jats:italic> = <jats:italic>C(r, m, f(r, m))<\/jats:italic> such that if <jats:italic>G<\/jats:italic> is a graph of order <jats:italic>n (n \u2265 r, n &gt; m)<\/jats:italic> with \u03b4<jats:sub><jats:italic>r<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) \u2265 (<jats:italic>n<\/jats:italic>\/3) + <jats:italic>C<\/jats:italic> and \u03b2 (<jats:italic>G<\/jats:italic>) \u2265 <jats:italic>f(r, m<\/jats:italic>), then (a) <jats:italic>G<\/jats:italic> is traceable if \u03b4(<jats:italic>G<\/jats:italic>) \u2265 <jats:italic>r<\/jats:italic> and <jats:italic>G<\/jats:italic> is connected; (b) <jats:italic>G<\/jats:italic> is hamiltonian if \u03b4(<jats:italic>G<\/jats:italic>) \u2265 <jats:italic>r<\/jats:italic> + 1 and <jats:italic>G<\/jats:italic> is 2\u2010connected; (c) <jats:italic>G<\/jats:italic> is hamiltonian\u2010connected if \u03b4(<jats:italic>G<\/jats:italic>) \u2265 <jats:italic>r<\/jats:italic> + 2 and <jats:italic>G<\/jats:italic> is 3\u2010connected. \u00a9 1995 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190190312","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T13:53:54Z","timestamp":1180187634000},"page":"397-409","source":"Crossref","is-referenced-by-count":7,"title":["Generalized degree conditions for graphs with bounded independence number"],"prefix":"10.1002","volume":"19","author":[{"given":"Ralph","family":"Faudree","sequence":"first","affiliation":[]},{"given":"Ronald J.","family":"Gould","sequence":"additional","affiliation":[]},{"given":"Linda","family":"Lesniak","sequence":"additional","affiliation":[]},{"given":"Terri","family":"Lindquester","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs & Digraphs","author":"Chartrand G.","year":"1986"},{"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":"10.1007\/BF02651085"},{"key":"e_1_2_1_5_2","unstructured":"L.Markus Hamiltonian results inK1 3\u2010free graphs. Preprint."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090208"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190190312","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190190312","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:58:08Z","timestamp":1698353888000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190190312"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,5]]}},"alternative-id":["10.1002\/jgt.3190190312"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190190312","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]]}}}