{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:02:43Z","timestamp":1775462563956,"version":"3.50.1"},"reference-count":3,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6700,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1988,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Bondy conjectured that if <jats:italic>G<\/jats:italic> is a <jats:italic>k<\/jats:italic>\u2010connected graph of order <jats:italic>n<\/jats:italic> such that\n<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>\nfor any (<jats:italic>k<\/jats:italic> + 1)\u2010independent set \/ of <jats:italic>G<\/jats:italic>, then the subgraph outside any longest cycle contains no path of length <jats:italic>k<\/jats:italic> \u2212 1. In this paper, we are going to prove that, if <jats:italic>G<\/jats:italic> is a <jats:italic>k<\/jats:italic>\u2010connected claw\u2010free (<jats:italic>K<\/jats:italic><jats:sub>1,3<\/jats:sub>\u2010free) graph of order <jats:italic>n<\/jats:italic> such that\n<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\/must002.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap>\nfor any (<jats:italic>k<\/jats:italic> + 1)\u2010independent set \/, then <jats:italic>G<\/jats:italic> contains a Hamilton cycle. The theorem in this paper implies Bondy's conjecture in the case of claw\u2010free graphs.<\/jats:p>","DOI":"10.1002\/jgt.3190120211","type":"journal-article","created":{"date-parts":[[2007,6,9]],"date-time":"2007-06-09T02:04:17Z","timestamp":1181354657000},"page":"209-216","source":"Crossref","is-referenced-by-count":41,"title":["Hamilton cycles in claw\u2010free graphs"],"prefix":"10.1002","volume":"12","author":[{"given":"Cun\u2010Quan","family":"Zhang","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":"J. A.Bondy Integrity in Graph Theory. The Theory of Applications of Graphs.117\u2013125."},{"key":"e_1_2_1_3_2","unstructured":"H. J.Broersma Sufficient conditions for hamiltonicity and traceability of K1 3\u2010free graphs. Preprint (1986)."},{"key":"e_1_2_1_4_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.3190120211","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190120211","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T17:55:54Z","timestamp":1697910954000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190120211"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,6]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1988,6]]}},"alternative-id":["10.1002\/jgt.3190120211"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190120211","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,6]]}}}