Optimizing weakly triangulated graphs
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An algorithm which runs inO((n + e)n3) time is presented which solves the maximum clique and minimum colouring problems for weakly triangulated graphs; performing the algorithm on the complement gives a solution to the maximum stable set and minimum clique covering problems.Abstract:
A graph is weakly triangulated if neither the graph nor its complement contains a chordless cycle with five or more vertices as an induced subgraph. We use a new characterization of weakly triangulated graphs to solve certain optimization problems for these graphs. Specifically, an algorithm which runs inO((n + e)n3) time is presented which solves the maximum clique and minimum colouring problems for weakly triangulated graphs; performing the algorithm on the complement gives a solution to the maximum stable set and minimum clique covering problems. Also, anO((n + e)n4) time algorithm is presented which solves the weighted versions of these problems.read more
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Book ChapterDOI
The maximum clique problem
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Journal ArticleDOI
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
Vincent Bouchitté,Ioan Todinca +1 more
TL;DR: It is shown that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum fill-in are polynomially tractable for these graphs.
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
Finding a maximum induced matching in weakly chordal graphs
TL;DR: It is shown that a maximum induced matching in a weakly chordal graph can be found in polynomial time and this generalizes previously known results for the induced matching problem.
Journal ArticleDOI
Algorithms for weakly triangulated graphs
Jeremy P. Spinrad,R. Sritharan +1 more
TL;DR: Improved algorithms for the recognition and the weighted versions of the optimization problems for the class of weakly triangulated graphs are presented.
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Weakly triangulated graphs
TL;DR: A class of graphs is introduced which includes both triangulated graphs and complements of triangulate graphs, and a structural theorem leads to a proof that weakly triangulation graphs are perfect.