A simple linear time algorithm for triangulating three-colored graphs

Abstract

In this paper we consider the problem of determining whether a given colored graph can be triangulated, such that no edges between vertices of the same color are added. This problem originated from the perfect phylogeny problem from molecular biology and is strongly related with the problem of recognizing partial k-trees. In this paper we give a simple linear time algorithm that solves the problem when there are three colors. We do this by first giving a complete structural characterization of the class of partial two-trees. © 1993 Academic Press, Inc.