Coloring a Graph Using Split Decomposition

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(n2 m) 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 Ck for some k ≥ 3.

• Type: Conference
• Year: 2004
• Where: WG
• Authors: Michaël Rao
• Keywords: Chromatic Number, Computer Science, Split Decomposition, Weighted Clique Number, WG 2004