{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:26:22Z","timestamp":1759335982762,"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>Let $G=(V,E)$ be any $d$-regular graph with girth $g$ on $n$ vertices, for $d \\geq 3$. This note shows that $G$ has a maximum matching which includes all but an exponentially small fraction of the vertices, $O((d-1)^{-g\/2})$.  Specifically, in a maximum matching of $G$, the number of unmatched vertices is at most $n\/n_0(d,g)$, where $n_0(d,g)$ is the number of vertices in a ball of radius $\\lfloor(g-1)\/2\\rfloor$ around a vertex, for odd values of $g$, and around an edge, for even values of $g$. This result is tight if $n  &lt; 2n_0(d,g)$.<\/jats:p>","DOI":"10.37236\/1002","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:52:29Z","timestamp":1578718349000},"source":"Crossref","is-referenced-by-count":14,"title":["Maximum Matchings in Regular Graphs of High Girth"],"prefix":"10.37236","volume":"14","author":[{"given":"Abraham D.","family":"Flaxman","sequence":"first","affiliation":[]},{"given":"Shlomo","family":"Hoory","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1n1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1n1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:05:06Z","timestamp":1579320306000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1n1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1002","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,3]]},"article-number":"N1"}}