{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T09:44:06Z","timestamp":1698227046674},"reference-count":15,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4449,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1994,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, <jats:italic>k<\/jats:italic> + 1 real numbers <jats:italic>c<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>c<\/jats:italic><jats:sub>2<\/jats:sub>, \u20db, <jats:italic>c<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic>+1<\/jats:sub> are found such that the following condition is sufficient for a <jats:italic>k<\/jats:italic>\u2010connected graph of order <jats:italic>n<\/jats:italic> to be hamiltonian: for each independent vertex set of <jats:italic>k<\/jats:italic> + 1 vertices in <jats:italic>G<\/jats:italic>.<\/jats:p><jats:p><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> where S<jats:sub>i<\/jats:sub> = {v \u2245 V:|N(v) \u2229 S| = i} for 0 \u2266 i \u2266 <jats:italic>k<\/jats:italic> + 1. Such a set of <jats:italic>k<\/jats:italic> + 1 numbers is called an <jats:italic>Hk<\/jats:italic>\u2010sequence. A sufficient condition for the existence of <jats:italic>Hk<\/jats:italic>\u2010sequences is obtained that generalizes many known results involving sum of degrees, neighborhood unions, and\/or neighborhood intersections.<\/jats:p>","DOI":"10.1002\/jgt.3190180508","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T17:50:59Z","timestamp":1181238659000},"page":"497-513","source":"Crossref","is-referenced-by-count":3,"title":["Hamiltonian graphs with neighborhood intersections"],"prefix":"10.1002","volume":"18","author":[{"given":"G.","family":"Chen","sequence":"first","affiliation":[]},{"given":"R. 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