Polynomial-time algorithms for minimum weighted colorings of ( P 5 , P 5 )-free graphs and similar graph classes
Chính T. Hoàng,D. Adam Lazzarato +1 more
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TLDR
An O ( n 3 ) algorithm to find a minimum weighted coloring of a ( P 5 , P � 5 )-free graph is designed and can be used to solve the same problem for several classes of graphs, defined by forbidden induced subgraphs, such as (diamond, co-diamond)-free graphs.About:
This article is published in Discrete Applied Mathematics.The article was published on 2015-05-11 and is currently open access. It has received 34 citations till now. The article focuses on the topics: Chordal graph & Indifference graph.read more
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Journal ArticleDOI
A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs
TL;DR: In this article, the authors survey known results on the computational complexity of k-coloring and k-COLORING for graph classes that are characterized by one or two forbidden induced subgraphs, and also consider a number of variants: for example, where the problem is to extend a partial coloring, or where lists of permissible colors are given for each vertex.
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A Survey on the Computational Complexity of Colouring Graphs with Forbidden Subgraphs
TL;DR: In this article, the authors survey known results on the computational complexity of coloring and coloring for graph classes that are characterized by one or two forbidden induced subgraphs, and also consider a number of variants: for example, where the problem is to extend a partial colouring, or where lists of permissible colours are given for each vertex.
Book ChapterDOI
Clique-Width of Graph Classes Defined by Two Forbidden Induced Subgraphs
TL;DR: This work considers classes characterized by forbidding a finite family of graphs as subgraphs, minors and topological minors, respectively, and completely determine which of these classes have bounded clique-width.
Journal ArticleDOI
Colouring diamond-free graphs.
TL;DR: The technique for handling this case is to reduce the graph under consideration to a $k$-partite graph that has a very specific decomposition, and this work is able to prove boundedness of clique-width for four other new classes of $(H_1,H_2)$-free graphs.
References
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The ellipsoid method and its consequences in combinatorial optimization
TL;DR: The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.
Journal ArticleDOI
Modular decomposition and transitive orientation
TL;DR: This work gives O(n+m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph and linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparable graphs and their complements.
Book ChapterDOI
A New Linear Algorithm for Modular Decomposition
Alain Cournier,Michel Habib +1 more
TL;DR: This work presents a new algorithm linear in time and space complexity for Modular Decomposition that builds and explores the decomposition tree of any undirected graph in a depth-first search way and shows that a vertex-splitting operation is really a central tool for modular decomposition algorithms.
Book ChapterDOI
Complexity of Coloring Graphs without Forbidden Induced Subgraphs
TL;DR: A complete characterization of parameter graphs H for which the problem of coloring H-free graphs is polynomial and for which it is NP-complete is given.
Journal ArticleDOI
Deciding k -Colorability of P 5 -Free Graphs in Polynomial Time
TL;DR: In this paper, it was shown that for every fixed integer k, there exists a polynomial-time algorithm for determining whether a P5-free graph admits a k-coloring, and finding one, if it does.