{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:19Z","timestamp":1753893859683,"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, the on-line list colouring of binomial random graphs $\\mathcal{G}(n,p)$ is studied. We show that the on-line choice number of $\\mathcal{G}(n,p)$ is asymptotically almost surely asymptotic to the chromatic number of $\\mathcal{G}(n,p)$, provided that the average degree $d=p(n-1)$ tends to infinity faster than $(\\log \\log n)^{1\/3} (\\log n)^2 n^{2\/3}$. For sparser graphs, we are slightly less successful; we show that if $d \\ge (\\log n)^{2+\\epsilon}$ for some $\\epsilon&gt;0$, then the on-line choice number is larger than the chromatic number by at most a multiplicative factor of $C$, where $C \\in [2,4]$, depending on the range of $d$. Also, for $d=O(1)$, the on-line choice number is by at most a multiplicative constant factor larger than the chromatic number.<\/jats:p>","DOI":"10.37236\/5003","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:47:34Z","timestamp":1578700054000},"source":"Crossref","is-referenced-by-count":1,"title":["On-line List Colouring of Random Graphs"],"prefix":"10.37236","volume":"22","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[]},{"given":"Dieter","family":"Mitsche","sequence":"additional","affiliation":[]},{"given":"Xavier","family":"P\u00e9rez-Gim\u00e9nez","sequence":"additional","affiliation":[]},{"given":"Pawe\u0142","family":"Pra\u0142at","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,6,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p41\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p41\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:15:58Z","timestamp":1579256158000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,3]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/5003","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,6,3]]},"article-number":"P2.41"}}