{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:57Z","timestamp":1753893777875,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we give new bounds on the bisection width of random 3-regular graphs on $n$ vertices. The main contribution is a new lower bound of $0.103295n$ based on a first moment method together with a structural analysis of the graph, thereby improving a 27-year-old result of Kostochka and Melnikov. We also give a complementary upper bound of $0.139822n$ by combining a result of Lyons with original combinatorial insights. Developping this approach further, we obtain a non-rigorous improved upper bound with the help of Monte Carlo simulations.<\/jats:p>","DOI":"10.37236\/11085","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T09:57:33Z","timestamp":1686909453000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Minimum Bisection of Random 3-Regular Graphs"],"prefix":"10.37236","volume":"30","author":[{"given":"Lyuben","family":"Lichev","sequence":"first","affiliation":[]},{"given":"Dieter","family":"Mitsche","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,6,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T09:57:33Z","timestamp":1686909453000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i2p40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,16]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/11085","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,6,16]]},"article-number":"P2.40"}}