Coloring a graph using split decomposition

Authors:
Michaël Rao
Affiliations:
Laboratoire d’Informatique Théorique et Appliquée, Université de Metz, Metz Cedex 01, France
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

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Abstract

We show how to use split decomposition to compute the weighted clique number and the chromatic number of a graph and we apply these results to some classes of graphs. In particular we present an O(n2m) algorithm to compute the chromatic number for all those graphs having a split decomposition in which every prime graph is an induced subgraph of either a Ck or a $\overline{C_k}$ for some k≥ 3.