{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T22:04:32Z","timestamp":1698357872947},"reference-count":9,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5056,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a <jats:italic>k<\/jats:italic>\u2010connected graph of order <jats:italic>n<\/jats:italic>. For an independent set c, let <jats:italic>d(S)<\/jats:italic> be the number of vertices adjacent to at least one vertex of <jats:italic>S<\/jats:italic> and &gt; let i(S) be the number of vertices adjacent to at least |S| vertices of <jats:italic>S<\/jats:italic>. We prove that if there exists some s, 1 \u2264 s \u2264 k, such that \u03a3<jats:sub>x<jats:italic>i<\/jats:italic>EX<\/jats:sub> d(X\\{X<jats:sub>i<\/jats:sub>}) &gt; s(n\u22121) \u2013 k[s\/2] \u2013 <jats:italic>i<\/jats:italic>(X)[(s\u22121)\/2] holds for every independetn set X ={x<jats:sub>0<\/jats:sub>, x<jats:sub>1<\/jats:sub> \u20dbx<jats:sub>s<\/jats:sub>} of s + 1 vertices, then <jats:italic>G<\/jats:italic> is hamiltonian. Several known results, including Fraisse's sufficient condition for hamiltonian graphs, are dervied as corollaries.<\/jats:p>","DOI":"10.1002\/jgt.3190160602","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T19:24:26Z","timestamp":1181244266000},"page":"529-543","source":"Crossref","is-referenced-by-count":16,"title":["An improvement of fraisse's sufficient condition for hamiltonian graphs"],"prefix":"10.1002","volume":"16","author":[{"given":"A.","family":"Ainouche","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","volume-title":"Graphs and Hypergraphs","author":"Berge C.","year":"1973"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190100316"},{"key":"e_1_2_1_4_2","unstructured":"A.Ainouche Connectivity independent sets and maximal circuits in undirected graphs. Ph.D. thesis London University (1980)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"e_1_2_1_6_2","article-title":"Hamiltonian properties of graphs with large neighborhood unions","author":"Bauer D.","journal-title":"Discrete Math."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(72)90079-9"},{"key":"e_1_2_1_8_2","first-page":"49","article-title":"On generalizing a theorem of Fraisse","volume":"29","author":"Schiermeyer I.","year":"1990","journal-title":"Ars Combinat."},{"key":"e_1_2_1_9_2","unstructured":"F.Tian A note on the paper \u201cA new sufficient condition for hamiltonian graph.\u201d Preprint (1989)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2308928"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190160602","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190160602","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T20:14:41Z","timestamp":1698092081000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190160602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,12]]},"references-count":9,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1992,12]]}},"alternative-id":["10.1002\/jgt.3190160602"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190160602","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,12]]}}}