{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822680,"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>We conjecture that any graph $G$ with treewidth $k$ and maximum degree $\\Delta(G)\\geq k + \\sqrt{k}$ satisfies $\\chi'(G)=\\Delta(G)$. In support of the conjecture we prove its fractional version.\u00a0We also show that any graph $G$ with treewidth $k\\geq 4$ and maximum degree $2k-1$ satisfies $\\chi'(G)=\\Delta(G)$, extending an old result of Vizing.<\/jats:p>","DOI":"10.37236\/6042","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:33:36Z","timestamp":1578670416000},"source":"Crossref","is-referenced-by-count":1,"title":["Chromatic Index, Treewidth and Maximum Degree"],"prefix":"10.37236","volume":"25","author":[{"given":"Henning","family":"Bruhn","sequence":"first","affiliation":[]},{"given":"Laura","family":"Gellert","sequence":"additional","affiliation":[]},{"given":"Richard","family":"Lang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,5,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:33:57Z","timestamp":1579235637000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,11]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/6042","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,5,11]]},"article-number":"P2.23"}}