{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:02Z","timestamp":1753893782153,"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>This note considers the problem of sampling from the set of weighted independent sets of a graph with maximum degree $\\Delta$. For a positive fugacity $\\lambda$, the weight of an independent set $\\sigma$ is $\\lambda^{|\\sigma|}$. Luby and Vigoda proved that the Glauber dynamics, which only changes the configuration at a randomly chosen vertex in each step, has mixing time $O(n\\log{n})$ when $\\lambda &lt; {{2}\\over {\\Delta-2}}$ for triangle-free graphs.  We extend their approach to general graphs.<\/jats:p>","DOI":"10.37236\/1552","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:09:21Z","timestamp":1578708561000},"source":"Crossref","is-referenced-by-count":43,"title":["A Note on the Glauber Dynamics for Sampling Independent Sets"],"prefix":"10.37236","volume":"8","author":[{"given":"Eric","family":"Vigoda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2001,1,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:20:22Z","timestamp":1579324822000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1552","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,1,17]]},"article-number":"R8"}}