{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:34Z","timestamp":1753893814809,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $H_n$ be a graph on $n$ vertices and let $\\overline{H_n}$ denote the complement of $H_n$. Suppose that $\\Delta = \\Delta(n)$ is the maximum degree of $\\overline{H_n}$. We analyse three algorithms for sampling $d$-regular subgraphs ($d$-factors) of $H_n$. This is equivalent to uniformly sampling $d$-regular graphs which avoid a set $E(\\overline{H_n})$ of forbidden edges. Here $d=d(n)$ is a positive integer which may depend on $n$.\r\nTwo of these algorithms produce a uniformly random $d$-factor of $H_n$ in expected runtime which is linear in $n$ and low-degree polynomial in $d$ and $\\Delta$. The first algorithm applies when $(d+\\Delta)d\\Delta = o(n)$. This improves on an earlier algorithm by the first author, which required constant $d$ and at most a linear number of edges in $\\overline{H_n}$. The second algorithm applies when $H_n$ is regular and $d^2+\\Delta^2 = o(n)$, adapting an approach developed by the first author together with Wormald. The third algorithm is a simplification of the second, and produces an approximately uniform $d$-factor of $H_n$ in time $O(dn)$.\u00a0 Here the output distribution differs from uniform by $o(1)$ in total variation distance, provided that $d^2+\\Delta^2 = o(n)$.<\/jats:p>","DOI":"10.37236\/8251","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:02:22Z","timestamp":1578636142000},"source":"Crossref","is-referenced-by-count":2,"title":["Uniform Generation of Spanning Regular Subgraphs of a Dense Graph"],"prefix":"10.37236","volume":"26","author":[{"given":"Pu","family":"Gao","sequence":"first","affiliation":[]},{"given":"Catherine","family":"Greenhill","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,11,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p28\/7952","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p28\/7952","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:01:41Z","timestamp":1579233701000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,8]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/8251","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,11,8]]},"article-number":"P4.28"}}