Triangulating graphs with few P4ʹs Original Research Article

A triangulation of a graph G is a chordal graph on the same vertex-set that contains G as a partial subgraph. In this paper we point out the use of the homogeneous decomposition of graphs for the purpose of triangulation. As a direct application we show how to compute in linear time the minimum fill-in and the treewidth of graphs which - in a certain local sense - contain only a small number of induced P4ʹs. Thereby, we extend and generalize known results about cographs.