{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:02Z","timestamp":1753893842480,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A graph $G$ is said to be $(k,m)$-choosable if for any assignment of $k$-element lists $L_v \\subset \\mathbb{R}$ to the vertices $v \\in V(G)$ and any assignment of $m$-element lists $L_e \\subset \\mathbb{R}$ to the edges $e \\in E(G)$\u00a0 there exists a total weighting $w: V(G) \\cup E(G) \\rightarrow \\mathbb{R}$ of $G$ such that $w(v) \\in L_v$ for any vertex $v \\in V(G)$ and $w(e) \\in L_e$ for any edge $e \\in E(G)$ and furthermore, such that for any pair of adjacent vertices $u,v$, we have $w(u)+ \\sum_{e \\in E(u)}w(e) \\neq w(v)+ \\sum_{e \\in E(v)}w(e)$, where $E(u)$ and $E(v)$ denote the edges incident to $u$ and $v$ respectively. In this paper we give an algorithmic proof showing that any graph $G$ without isolated edges is $(1, 2 \\lceil \\log_2(\\Delta(G)) \\rceil+1)$-choosable, where $\\Delta(G)$ denotes the maximum degree in $G$.<\/jats:p>","DOI":"10.37236\/6878","type":"journal-article","created":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T02:34:39Z","timestamp":1619145279000},"source":"Crossref","is-referenced-by-count":1,"title":["Vertex Colouring Edge Weightings: a Logarithmic Upper Bound on Weight-Choosability"],"prefix":"10.37236","volume":"28","author":[{"given":"Kasper Szabo","family":"Lyngsie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Zhong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,4,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T02:34:39Z","timestamp":1619145279000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i2p11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,23]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/6878","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,4,23]]},"article-number":"P2.11"}}