{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T14:48:32Z","timestamp":1769093312356,"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>The edges of the complete graph $K_n$ are coloured so that no colour appears more than $\\lceil cn\\rceil$ times, where $c &lt; 1\/32$ is a constant. We show that if $n$ is sufficiently large then  there is a Hamiltonian cycle in which each  edge is a different colour, thereby proving a 1986 conjecture of Hahn and Thomassen.  We prove a similar result for the complete digraph with $c &lt; 1\/64$.  We also show, by essentially the same technique, that if $t\\geq 3$, $c &lt; (2t^2(1+t))^{-1}$, no  colour appears more than $\\lceil cn\\rceil$ times and $t|n$ then the vertices can be partitioned into $n\/t$ $t-$sets $K_1,K_2,\\ldots,K_{n\/t}$ such that the colours of the $n(t-1)\/2$ edges contained in the $K_i$'s are distinct. The proof technique follows the lines of Erd\u0151s and Spencer's modification of the Local Lemma.<\/jats:p>","DOI":"10.37236\/1204","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:26:06Z","timestamp":1578705966000},"source":"Crossref","is-referenced-by-count":48,"title":["Multicoloured Hamilton Cycles"],"prefix":"10.37236","volume":"2","author":[{"given":"Michael","family":"Albert","sequence":"first","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]},{"given":"Bruce","family":"Reed","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,5,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r10\/comment","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:32:08Z","timestamp":1579339928000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v2i1r10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1995,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1204","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5,9]]},"article-number":"R10"}}