{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:31:38Z","timestamp":1761611498057,"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>It is proved that, if $G$ is a $K_4$-minor-free graph with maximum degree $\\Delta \\ge 4$, then $G$ is totally $(\\Delta+1)$-choosable; that is, if every element (vertex or edge) of $G$ is assigned a list of $\\Delta+1$ colours, then every element can be coloured with a colour from its own list in such a way that every two adjacent or incident elements are coloured with different colours.  Together with other known results, this shows that the List-Total-Colouring Conjecture, that ${\\rm ch}\"(G) = \\chi\"(G)$ for every graph $G$, is true for all $K_4$-minor-free graphs.  The List-Edge-Colouring Conjecture is also known to be true for these graphs.  As a fairly straightforward consequence, it is proved that both conjectures hold also for all $K_{2,3}$-minor free graphs and all $(\\bar K_2 + (K_1 \\cup K_2))$-minor-free graphs.<\/jats:p>","DOI":"10.37236\/1124","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:55:59Z","timestamp":1578718559000},"source":"Crossref","is-referenced-by-count":7,"title":["Edge and Total Choosability of Near-Outerplanar Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Timothy J.","family":"Hetherington","sequence":"first","affiliation":[]},{"given":"Douglas R.","family":"Woodall","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,10,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r98\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r98\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:06:56Z","timestamp":1579320416000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r98"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1124","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,10,31]]},"article-number":"R98"}}