{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T05:12:37Z","timestamp":1754111557649,"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>A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices $v$, $w$ the set of colours appearing on the edges incident with $v$ is not equal to the set of colours appearing on the edges incident with $w$.  Let ${\\rm ndi}(G)$ be the least number of colours required for a proper neighbour-distinguishing edge colouring of $G$.  We prove that for $d\\geq 4$, a random $d$-regular graph $G$ on $n$ vertices asymptotically almost surely satisfies ${\\rm ndi}(G)\\leq \\lceil 3d\/2\\rceil$.  This verifies a conjecture of Zhang, Liu and Wang for almost all 4-regular graphs.<\/jats:p>","DOI":"10.37236\/1103","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:58:47Z","timestamp":1578718727000},"source":"Crossref","is-referenced-by-count":11,"title":["Neighbour$\\,$&amp;ndash;$\\,$Distinguishing Edge Colourings of Random Regular Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Catherine","family":"Greenhill","sequence":"first","affiliation":[]},{"given":"Andrzej","family":"Ruci\u0144ski","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,8,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r77\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r77\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:08:09Z","timestamp":1579320489000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r77"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1103","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,8,25]]},"article-number":"R77"}}