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- W2953292089 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2011 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)The stubborn problem is stubborn no more (a polynomial algorithm for 3–compatible colouring and the stubborn list partition problem)Marek Cygan, Marcin Pilipczuk, Michal Pilipczuk, and Jakub Onufry WojtaszczykMarek CyganDept. of Mathematics, Computer Science and Mechanics, University of Warsaw, PolandSearch for more papers by this author, Marcin PilipczukDept. of Mathematics, Computer Science and Mechanics, University of Warsaw, PolandSearch for more papers by this author, Michal PilipczukDept. of Mathematics, Computer Science and Mechanics, University of Warsaw, PolandSearch for more papers by this author, and Jakub Onufry WojtaszczykDept. of Mathematics, Computer Science and Mechanics, University of Warsaw, PolandSearch for more papers by this authorpp.1666 - 1674Chapter DOI:https://doi.org/10.1137/1.9781611973082.128PDFBibTexSections ToolsAdd to favoritesDownload CitationsTrack CitationsEmail SectionsAboutAbstract We present a polynomial time algorithm for the 3-Compatible colouring problem, where we are given a complete graph with each edge assigned one of 3 possible colours and we want to assign one of those 3 colours to each vertex in such a way that no edge has the same colour as both of its endpoints. Consequently we complete the proof of a dichotomy for the k-Compatible Colouring problem. The tractability of the 3-Compatible colouring problem has been open for several years and the best known algorithm prior to this paper is due to Feder et al. [SODA'05] — a quasipolynomial algorithm with a nO(log n/log log n) time complexity. Furthermore our result implies a polynomial algorithm for the Stubborn problem which enables us to finish the classification of all List Matrix Partition variants for matrices of size at most four over subsets of {0, 1} started by Cameron et al. [SODA'04]. Previous chapter Next chapter RelatedDetails Published:2011ISBN:978-0-89871-993-2eISBN:978-1-61197-308-2 https://doi.org/10.1137/1.9781611973082Book Series Name:ProceedingsBook Code:PR138Book Pages:xviii-1788" @default.
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- W2953292089 title "The stubborn problem is stubborn no more (a polynomial algorithm for 3–compatible colouring and the stubborn list partition problem)" @default.
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