{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:28Z","timestamp":1753893808614,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In [Graphs Combin. 24 (2008) 469\u2013483], the third author and the fifth author conjectured that if $G$ is a $k$-connected graph such that $\\sigma_{k+1}(G) \\ge |V(G)|+\\kappa(G)+(k-2)(\\alpha(G)-1)$, then $G$ contains a Hamilton cycle, where $\\sigma_{k+1}(G)$, $\\kappa(G)$ and $\\alpha(G)$ are the minimum degree sum of $k+1$ independent vertices, the connectivity and the independence number of $G$, respectively. In this paper, we settle this conjecture. The degree sum condition is best possible.\r\n\u00a0<\/jats:p>","DOI":"10.37236\/5480","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:59:31Z","timestamp":1578617971000},"source":"Crossref","is-referenced-by-count":0,"title":["A Degree Sum Condition on the Order, the Connectivity and the Independence Number for Hamiltonicity"],"prefix":"10.37236","volume":"26","author":[{"given":"Shuya","family":"Chiba","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michitaka","family":"Furuya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenta","family":"Ozeki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masao","family":"Tsugaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomoki","family":"Yamashita","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2019,12,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p53\/7984","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p53\/7984","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:00:15Z","timestamp":1579215615000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5480","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,12,20]]},"article-number":"P4.53"}}