Treewidth: Computations and Approximations

Ton Kloks (eds.)3540583564, 9783540583561

This treatise investigates a number of problems related to treewidth and pathwidth of graphs. The main objective is to obtain good bounds on the complexity of determining the treewidth and pathwidth for various classes of graphs.
Originating from the author’s Ph.D. thesis, this monograph presents original own work. Nevertheless, many interesting perspectives beyond are presented. In total, the book is a smooth introduction to the topic of graphs of bounded treewidth. It will help to satisfy the strong interest among the algorithmic graph theory community in the theory pertaining to the topic. Particularly valuable is the thorough survey given of the relevant current literature.

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Table of contents :
Introduction and basic terminology….Pages 1-6
Preliminaries….Pages 7-25
Testing superperfection of k-trees….Pages 27-38
Triangulating 3-colored graphs….Pages 39-50
Only few graphs have bounded treewidth….Pages 51-60
Approximating treewidth and pathwidth of a graph….Pages 61-74
Approximating treewidth and pathwidth for some classes of perfect graphs….Pages 75-91
Treewidth of chordal bipartite graphs….Pages 93-104
Treewidth and pathwidth of permutation graphs….Pages 105-115
Treewidth of circle graphs….Pages 117-124
Finding all minimal separators of a graph….Pages 125-135
Treewidth and pathwidth of cocomparability graphs of bounded dimension….Pages 137-146
Pathwidth of pathwidth-bounded graphs….Pages 147-172
Treewidth of treewidth-bounded graphs….Pages 173-183
Recognizing treewidth-bounded graphs….Pages 185-192