{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:50Z","timestamp":1753893770212,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A simple, undirected $2$-connected graph $G$ of order $n$ belongs to class ${\\cal O}(n$,$\\varphi)$, $\\varphi\\geq0$, if $\\sigma_{2}=n-\\varphi.$ It is well known (Ore's theorem) that $G$ is hamiltonian if $\\varphi= 0$, in which case the $2$-connectedness hypothesis is implied. In this paper we provide a method for studying this class of graphs. As an application we give a full characterization of graphs $G$ in ${\\cal O}(n$,$\\varphi)$, $\\varphi\\leq3$, in terms of their dual hamiltonian closure.<\/jats:p>","DOI":"10.37236\/1086","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:59:30Z","timestamp":1578700770000},"source":"Crossref","is-referenced-by-count":0,"title":["Relaxations of Ore's Condition on Cycles"],"prefix":"10.37236","volume":"13","author":[{"given":"Ahmed","family":"Ainouche","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,7,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r60\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r60\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:10:19Z","timestamp":1579302619000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1086","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,7,28]]},"article-number":"R60"}}