{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:47Z","timestamp":1753893827872,"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>The pegging algorithm is a method of generating large random regular graphs beginning with small ones. The $\\epsilon$-mixing time of the distribution of short cycle counts of these random regular graphs is the time at which the distribution reaches and maintains total variation distance at most $\\epsilon$ from its limiting distribution. We show that this $\\epsilon$-mixing time is not $o(\\epsilon^{-1})$. This demonstrates that the upper bound $O(\\epsilon^{-1})$ proved recently by the authors is essentially tight.<\/jats:p>","DOI":"10.37236\/133","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:32:30Z","timestamp":1578717150000},"source":"Crossref","is-referenced-by-count":2,"title":["Rate of Convergence of the Short Cycle Distribution in Random Regular Graphs Generated by Pegging"],"prefix":"10.37236","volume":"16","author":[{"given":"Pu","family":"Gao","sequence":"first","affiliation":[]},{"given":"Nicholas","family":"Wormald","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:05:02Z","timestamp":1579316702000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/133","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,3,31]]},"article-number":"R44"}}