The NP-Completeness of Edge-Coloring

Abstract

Previous article Next article The NP-Completeness of Edge-ColoringIan HolyerIan Holyerhttps://doi.org/10.1137/0210055PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractWe show that it is NP-complete to determine the chromatic index of an arbitrary graph. The problem remains NP-complete even for cubic graphs.[1] S. Fiorini and , Robin James Wilson, Edge-colourings of graphs, Pitman, London, 1977iii+154 58:27599 0421.05023 Google Scholar[2] Michael R. Garey and , David S. Johnson, Computers and intractability, W. H. Freeman and Co., San Francisco, Calif., 1979x+338 80g:68056 0411.68039 Google Scholar[3] Rufus Isaacs, Infinite families of nontrivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly, 82 (1975), 221–239 52:2940 0311.05109 CrossrefISIGoogle Scholar[4] R. Isaacs, Loupekine's snarks: A bifamily of non-Tait-colorable graphs, unpublished Google ScholarKeywordscomputational complexityNP-complete problemschromatic indexedge-coloring Previous article Next article FiguresRelatedReferencesCited ByDetails Regular pattern-free coloringDiscrete Applied Mathematics, Vol. 321 | 1 Nov 2022 Cross Ref Chromatic index of dense quasirandom graphsJournal of Combinatorial Theory, Series B, Vol. 157 | 1 Nov 2022 Cross Ref Subcubic planar graphs of girth 7 are class IDiscrete Mathematics, Vol. 345, No. 10 | 1 Oct 2022 Cross Ref Independence number of edge‐chromatic critical graphsJournal of Graph Theory, Vol. 101, No. 2 | 20 March 2022 Cross Ref Complexity Dichotomy for List-5-Coloring with a Forbidden Induced SubgraphSepehr Hajebi, Yanjia Li, and Sophie SpirklSIAM Journal on Discrete Mathematics, Vol. 36, No. 3 | 30 August 2022AbstractPDF (592 KB)The Overfullness of Graphs with Small Minimum Degree and Large Maximum DegreeYan Cao, Guantao Chen, Guangming 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