{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:32:05Z","timestamp":1764174725830,"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>The Ohba Conjecture says that every graph $G$ with $|V(G)| \\le 2 \\chi(G)+1$ is chromatic choosable. This paper studies an on-line version of Ohba Conjecture. We prove that unlike the off-line case, for $k \\ge 3$, the complete multipartite graph $K_{2\\star (k-1), 3}$ is not on-line chromatic-choosable. Based on this result, the on-line version of Ohba Conjecture is modified as follows: Every graph $G$ with $|V(G)| \\le 2 \\chi(G)$ is on-line chromatic choosable. We present an explicit strategy to show\u00a0 that for any positive integer $k$, the graph $K_{2\\star k}$ is on-line chromatic-choosable.\u00a0 We then present a minimal function $g$ for which the graph $K_{2 \\star (k-1), 3}$ is on-line $g$-choosable.<\/jats:p>","DOI":"10.37236\/2050","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:32:07Z","timestamp":1578713527000},"source":"Crossref","is-referenced-by-count":10,"title":["On-Line List Colouring of Complete Multipartite Graphs"],"prefix":"10.37236","volume":"19","author":[{"given":"Seog-Jin","family":"Kim","sequence":"first","affiliation":[]},{"given":"Young Soo","family":"Kwon","sequence":"additional","affiliation":[]},{"given":"Daphne Der-Fen","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Xuding","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,2,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p41\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p41\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:41:51Z","timestamp":1579300911000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/2050","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,2,23]]},"article-number":"P41"}}