Upper bounds to the clique width of graphs

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Abstract

Hierarchical decompositions of graphs are interesting for algorithmic purposes. Many NP complete problems have linear complexity on graphs with tree-decompositions of bounded width. We investigate alternate hierarchical decompositions that apply to wider classes of graphs and still enjoy good algorithmic properties. These decompositions are motivated and inspired by the study of vertex-replacement context-free graph grammars. The complexity measure of graphs associated with these decompositions is called clique width. In this paper we bound the clique width of a graph in terms of its tree width on the one hand, and of the clique width of its edge complement on the other.

Keywords

Hierarchical graph decompositions
Modular decomposition
Tree decompositions
Algorithms
Monadic second-order logic

Cited by (0)

Work supported in part by NSF grant CCR-9522093 and by ONR grant N00014-97-1-0526.

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http://dept-info.labri.u-bordeaux.fr/∼courcell/ActSci.html.