{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T12:29:10Z","timestamp":1772368150687,"version":"3.50.1"},"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 super $(d,\\epsilon)$-regular graph on $2n$ vertices is a bipartite graph on the classes of vertices $V_1$ and $V_2$, where $|V_1|=|V_2|=n$, in which the minimum degree and the maximum degree are between  $ (d-\\epsilon)n$ and $ (d+\\epsilon) n$, and for every $U \\subset V_1, W \\subset V_2$ with $|U| \\geq \\epsilon n$, $|W| \\geq \\epsilon n$, $|{{e(U,W) }\\over{|U||W|}}-{{e(V_1,V_2)}\\over{|V_1||V_2|}}|  &lt;  \\epsilon.$ We prove that for every $1&gt;d &gt;2 \\epsilon &gt;0$ and $n&gt;n_0(\\epsilon)$, the number of perfect matchings in any such graph is at least $(d-2\\epsilon)^n n!$ and at most $(d+2 \\epsilon)^n n!$.  The proof relies on the validity of two well known conjectures  for permanents; the Minc conjecture, proved by Br\u00e9gman, and  the van der Waerden conjecture, proved by Falikman and Egorichev. <\/jats:p>","DOI":"10.37236\/1351","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:58:08Z","timestamp":1578689888000},"source":"Crossref","is-referenced-by-count":9,"title":["Perfect Matchings in $\\epsilon$-regular Graphs"],"prefix":"10.37236","volume":"5","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[]},{"given":"Vojtech","family":"R\u00f6dl","sequence":"additional","affiliation":[]},{"given":"Andrzej","family":"Ruci\u0144ski","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1998,2,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v5i1r13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v5i1r13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T01:10:39Z","timestamp":1579309839000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v5i1r13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,2,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1998,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1351","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,2,8]]},"article-number":"R13"}}