{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T06:54:41Z","timestamp":1768719281739,"version":"3.49.0"},"reference-count":14,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":3962,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we investigate the Hamiltonicity of <jats:italic>K<\/jats:italic><jats:sub>1,r<\/jats:sub>\u2010free graphs with some degree conditions. In particular, let <jats:italic>G<\/jats:italic> be a <jats:italic>k<\/jats:italic>\u2010connected grph of order <jats:italic>n<\/jats:italic>\u22673 which is <jats:italic>K<\/jats:italic><jats:sub>1,4<\/jats:sub>\u2010free. If <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> for every independent set {<jats:italic>v<\/jats:italic><jats:sub>0<\/jats:sub>, <jats:italic>v<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026, <jats:italic>v<\/jats:italic><jats:sub>k<\/jats:sub>} then <jats:italic>G<\/jats:italic> is hamiltonian. We use an upper bound for the independence number of <jats:italic>K<\/jats:italic><jats:sub>1,r<\/jats:sub>\u2010free graphs to extent the above result to <jats:italic>K<\/jats:italic><jats:sub>1,r<\/jats:sub>\u2010free graphs. Hamiltonian connected and, more generally, <jats:italic>q<\/jats:italic>\u2010edge hamiltonian properties are studied here as well. \u00a9 1995 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190200406","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T15:26:32Z","timestamp":1181229992000},"page":"423-439","source":"Crossref","is-referenced-by-count":13,"title":["Hamiltonicity for <i>K<\/i><sub>1, r<\/sub>\u2010free graphs"],"prefix":"10.1002","volume":"20","author":[{"given":"Guantao","family":"Chen","sequence":"first","affiliation":[]},{"given":"R. H.","family":"Schelp","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"117","volume-title":"The Theory and Applications of Graphs","author":"Bondy J. A.","year":"1981"},{"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","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195323"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(72)90079-9"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(73)90138-6"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90078-4"},{"key":"e_1_2_1_8_2","first-page":"82","article-title":"Problem 5","volume":"4","author":"Lov\u00e1sz L.","year":"1974","journal-title":"Period. Math. Hungary"},{"key":"e_1_2_1_9_2","unstructured":"L. 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Pure Appl."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120211"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190200406","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190200406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T17:42:28Z","timestamp":1698255748000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190200406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["10.1002\/jgt.3190200406"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190200406","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}