{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:41:17Z","timestamp":1768740077671,"version":"3.49.0"},"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>We consider the distribution of cycle counts in a random regular\u00a0graph, which is closely linked to the graph's spectral properties.\u00a0We broaden the asymptotic regime in which the cycle counts\u00a0are known to be\u00a0approximately Poisson, and we give an explicit bound\u00a0in total variation distance for the approximation. Using this result,\u00a0we calculate limiting distributions of linear eigenvalue statistics\u00a0for random regular graphs.  Previous results on the distribution of\u00a0cycle counts by McKay, Wormald, and Wysocka (2004) used the method of\u00a0switchings, a combinatorial technique for asymptotic enumeration. Our\u00a0proof uses Stein's method of exchangeable pairs and demonstrates\u00a0an interesting connection between the two techniques.<\/jats:p>","DOI":"10.37236\/4659","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:31:49Z","timestamp":1578702709000},"source":"Crossref","is-referenced-by-count":8,"title":["Exchangeable Pairs, Switchings, and Random Regular Graphs"],"prefix":"10.37236","volume":"22","author":[{"given":"Tobias","family":"Johnson","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,2,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:37:04Z","timestamp":1579257424000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4659","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,16]]},"article-number":"P1.33"}}