{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:47:58Z","timestamp":1759063678098,"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>Let $G$ be a simple graph with $3\\Delta (G) &gt; |V|$. The Overfull Graph Conjecture states that the chromatic index of $G$ is equal to $\\Delta (G)$, if $G$ does not contain an induced overfull subgraph $H$ with $\\Delta (H) = \\Delta (G)$, and otherwise it is equal to $\\Delta (G) +1$. We present an algorithm that determines these subgraphs in $O(n^{5\/3}m)$ time, in general, and in $O(n^3)$ time, if $G$ is regular. Moreover, it is shown that $G$ can have at most three of these subgraphs. If $2\\Delta (G) \\geq |V|$, then $G$ contains at most one of these subgraphs, and our former algorithm for this situation is improved to run in linear time.<\/jats:p>","DOI":"10.37236\/1551","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:09:36Z","timestamp":1578690576000},"source":"Crossref","is-referenced-by-count":6,"title":["How to Find Overfull Subgraphs in Graphs with Large Maximum Degree, II"],"prefix":"10.37236","volume":"8","author":[{"given":"Thomas","family":"Niessen","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,12,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:20:37Z","timestamp":1579306837000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1551","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,12,10]]},"article-number":"R7"}}