Contribution
Triangulating graphs with few P4's

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Abstract

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 P4's. Thereby, we extend and generalize known results about cographs.

Keywords

Triangulation
Minimum fill-in
Treewidth
Homogeneous decomposition
Graphs with few P4's

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Supported by the Deutsche Forschungsgemeinschaft (DFG).

This work was done while the author was visiting University of Graz, Austria.