{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:27:36Z","timestamp":1775464056947,"version":"3.50.1"},"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>Suppose $G$ is $r$-colorable and $P \\subseteq V(G)$ is such that  the components of $G[P]$ are far apart.  We show that any  $(r+s)$-coloring of $G[P]$ in which each component is $s$-colored extends to an $(r+s)$-coloring of $G$.   If $G$ does not contract to $K_5$ or is planar and $s \\geq 2$, then any $(r+s-1)$-coloring of $P$ in which each component is $s$-colored extends to an $(r+s-1)$-coloring of $G$. This result uses the Four Color Theorem and its equivalence to Hadwiger's Conjecture for $k = 5$. For $s=2$ this provides an affirmative answer to a question of Thomassen.  Similar results hold for coloring arbitrary graphs embedded in both orientable and non-orientable surfaces.<\/jats:p>","DOI":"10.37236\/1653","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:25:21Z","timestamp":1578709521000},"source":"Crossref","is-referenced-by-count":11,"title":["Graph Color Extensions:  When Hadwiger's Conjecture and Embeddings Help"],"prefix":"10.37236","volume":"9","author":[{"given":"Michael O.","family":"Albertson","sequence":"first","affiliation":[]},{"given":"Joan P.","family":"Hutchinson","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2002,9,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:13:30Z","timestamp":1579324410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1r37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1653","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9,12]]},"article-number":"R37"}}