{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:32:27Z","timestamp":1764174747542,"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>This paper studies on-line list colouring of graphs. It is proved that the on-line choice number of a graph $G$ on $n$ vertices is at most $\\chi(G) \\ln n+1$, and the on-line $b$-choice number of $G$ is at most ${e\\chi(G)-1\\over e-1} (b-1+ \\ln n)+b$.  Suppose $G$ is a graph with a given $\\chi(G)$-colouring of $G$. Then for any $(\\chi(G) \\ln n +1)$-assignment $L$ of $G$, we give a polynomial time algorithm which constructs an $L$-colouring of $G$. For any $({e\\chi(G)-1\\over e-1} (b-1+ \\ln n)+b)$-assignment $L$ of $G$, we give a polynomial time algorithm which constructs an $(L,b)$-colouring of $G$. We then characterize all on-line $2$-choosable graphs. It is also proved that a complete bipartite graph of the form $K_{3,q}$ is on-line $3$-choosable if and only if it is $3$-choosable, but there are graphs of the form $K_{6,q}$ which are $3$-choosable but not on-line $3$-choosable. Some open questions concerning on-line list colouring are posed in the last section.<\/jats:p>","DOI":"10.37236\/216","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:24:30Z","timestamp":1578716670000},"source":"Crossref","is-referenced-by-count":43,"title":["On-Line List Colouring of Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Xuding","family":"Zhu","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,10,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r127\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:40:14Z","timestamp":1579315214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/216","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,10,19]]},"article-number":"R127"}}