{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:27:34Z","timestamp":1775464054357,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a graph embedded on a surface $S_\\varepsilon$ with Euler genus $\\varepsilon &gt; 0$, and let $P\\subset V(G)$ be a set of vertices mutually at distance at least 4 apart. Suppose all vertices of $G$ have $H(\\varepsilon)$-lists and the vertices of $P$ are precolored, where $H(\\varepsilon)=\\Big\\lfloor\\frac{7 + \\sqrt{24\\varepsilon + 1}}{2}\\Big\\rfloor$ is the Heawood number. We show that the coloring of $P$ extends to a list-coloring of $G$ and that the distance bound of 4 is best possible. Our result provides an answer to an analogous question of Albertson about extending a precoloring of a set of mutually distant vertices in a planar graph to a 5-list-coloring of the graph and generalizes a result of Albertson and Hutchinson to list-coloring extensions on surfaces.<\/jats:p>","DOI":"10.37236\/2487","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:09:43Z","timestamp":1578694183000},"source":"Crossref","is-referenced-by-count":1,"title":["List-Coloring Graphs on Surfaces with Varying List-Sizes"],"prefix":"10.37236","volume":"19","author":[{"given":"Alice M.","family":"Dean","sequence":"first","affiliation":[]},{"given":"Joan P.","family":"Hutchinson","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,12,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p50\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p50\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:21:09Z","timestamp":1579281669000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,31]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2487","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,31]]},"article-number":"P50"}}