{"title":"Algorithms for edge coloring bipartite graphs","authors":"H. Gabow, O. Kariv","doi":"10.1145/800133.804346","DOIUrl":null,"url":null,"abstract":"A minimum edge coloring of a bipartite graph is a partition of the edges into &Dgr; matchings, where &Dgr; is the maximum degree in the graph. Coloring algorithms are presented that use time O(min(¦E¦ &Dgr; log n, ¦E¦ @@@@n log n, n2log &Dgr;)) and space O(n&Dgr;). This compares favorably to the previous O(¦E¦ [equation] log &Dgr;) time bound. The coloring algorithms also find maximum matchings on regular (or semi-regular) bipartite graphs. The time bounds compare favorably to the O(¦E¦ @@@@n) matching algorithm, expect when [equation] ≤ &Dgr; ≤ @@@@n log n.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the tenth annual ACM symposium on Theory of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800133.804346","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 29
Abstract
A minimum edge coloring of a bipartite graph is a partition of the edges into &Dgr; matchings, where &Dgr; is the maximum degree in the graph. Coloring algorithms are presented that use time O(min(¦E¦ &Dgr; log n, ¦E¦ @@@@n log n, n2log &Dgr;)) and space O(n&Dgr;). This compares favorably to the previous O(¦E¦ [equation] log &Dgr;) time bound. The coloring algorithms also find maximum matchings on regular (or semi-regular) bipartite graphs. The time bounds compare favorably to the O(¦E¦ @@@@n) matching algorithm, expect when [equation] ≤ &Dgr; ≤ @@@@n log n.