{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:00Z","timestamp":1753893780835,"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 graph $G=(V,E)$ on $n$ vertices is super $\\epsilon$-regular if (i) all vertices have degree in the range $[(d-\\epsilon)n,(d+\\epsilon)n]$, $dn$ being the average degree, and (ii) for every pair of disjoint sets $S,T\\subseteq V,\\,|S|,|T|\\geq \\epsilon n$, $e(S,T)$ is in the range $[(d-\\epsilon)|S||T|,(d+\\epsilon)|S||T|]$. We show that the number of perfect matchings lies in the range $$[((d-2\\epsilon)^\\nu {{n!}\\over {\\nu !2^\\nu}},(d+2\\epsilon)^\\nu {{n!}\\over {\\nu !2^\\nu}}],$$ where $\\nu ={{n}\\over {2}}$, and the number of Hamilton cycles lies in the range $[(d-2\\epsilon)^nn!,(d+2\\epsilon)^nn!]$.<\/jats:p>","DOI":"10.37236\/1535","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:02:27Z","timestamp":1578708147000},"source":"Crossref","is-referenced-by-count":7,"title":["On the Number of Perfect Matchings and Hamilton Cycles in $\\epsilon$-Regular Non-bipartite Graphs"],"prefix":"10.37236","volume":"7","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,11,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r57\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r57\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:20:50Z","timestamp":1579324850000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,11,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1535","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,11,19]]},"article-number":"R57"}}