{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:12:47Z","timestamp":1772136767787,"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>Given a graph $G$ and $p\\in [0,1]$, the random subgraph $G_p$ is obtained by retaining each edge of $G$ independently with probability $p$. We show that for every $\\epsilon&gt;0$, there exists a constant $C&gt;0$ such that the following holds. Let $d\\ge C$ be an integer, let $G$ be a $d$-regular graph and let $p\\ge \\frac{C}{d}$. Then, with probability tending to one as $|V(G)|$ tends to infinity, there exists a matching in $G_p$ covering at least $(1-\\epsilon)|V(G)|$ vertices.\r\nWe further show that for a wide family of $d$-regular graphs $G$, which includes the $d$-dimensional hypercube, for any $p\\ge \\frac{\\log^5d}{d}$ with probability tending to one as $d$ tends to infinity, $G_p$ contains an induced subgraph on at least $(1-o(1))|V(G)|$ vertices, whose degrees are tightly concentrated around the expected average degree $dp$.<\/jats:p>","DOI":"10.37236\/14036","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:30Z","timestamp":1772135010000},"source":"Crossref","is-referenced-by-count":0,"title":["Large Matchings and nearly Spanning, nearly Regular Subgraphs of Random Subgraphs"],"prefix":"10.37236","volume":"33","author":[{"given":"Sahar","family":"Diskin","sequence":"first","affiliation":[]},{"given":"Joshua","family":"Erde","sequence":"additional","affiliation":[]},{"given":"Mihyun","family":"Kang","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Krivelevich","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,2,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:30Z","timestamp":1772135010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/14036","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,27]]},"article-number":"P1.37"}}