Constructions of k -critical P 5 -free graphs
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An infinite set of k -critical P 5 -free graphs for every k -chromatic graph G ?About:
This article is published in Discrete Applied Mathematics.The article was published on 2015-02-19 and is currently open access. It has received 37 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.
Journal ArticleDOI
Complexity of coloring graphs without paths and cycles
Pavol Hell,Shenwei Huang +1 more
TL;DR: This paper shows that in most other cases the k-COLORING problem for (P t ,C l)-free graphs is NP-complete, and proves that there are only finitely many minimal non-k-colorable (P 6,C 4)- free graphs for any fixed k; however, the algorithms do not have the explicit lists for higher k, and thus no certifying algorithms.
Journal ArticleDOI
Exhaustive generation of k-critical H-free graphs
Jan Goedgebeur,Oliver Schaudt +1 more
TL;DR: An algorithm for generating all k-critical H-free graphs is described, and it is proved that there are only finitely many 4-critical (P7,Ck)-free graphs, and every P11-free graph of girth at least five is 3-colorable.
Book ChapterDOI
Complexity of Coloring Graphs without Paths and Cycles
Pavol Hell,Shenwei Huang +1 more
TL;DR: This paper shows that in most other cases the k-COLORING problem for (P t ,C l)-free graphs is NP-complete, and proves that there are only finitely many minimal non-k-colorable (P 6,C 4)- free graphs for any fixed k; however, the algorithms do not have the explicit lists for higher k, and thus no certifying algorithms.
References
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Journal ArticleDOI
The Strong Perfect Graph Theorem
TL;DR: The strong perfect graph conjecture as discussed by the authors states that a graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced sub graph of G is an odd cycle of length at least five or the complement of one.
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.
Journal ArticleDOI
3-Colorability ∈ P for P 6 -free graphs
Bert Randerath,Ingo Schiermeyer +1 more
TL;DR: In this paper, it was shown that 3-colorability can be decided in polynomial time for the class of P6-free graphs with bounded dominating subgraphs.