TREEWIDTH OF CIRCLE GRAPHS

Abstract

In this paper we show that the treewidth of a circle graph can be computed in polynomial time. A circle graph is a graph that is isomorphic to the intersection graph of a finite collection of chords of a circle. The TREEWIDTH problem can be viewed upon as the problem of finding a chordal embedding of the graph that minimizes the clique number. Our algorithm to determine the treewidth of a circle graph can be implemented to run in O(n 3 ) time, where n is the number of vertices of the graph.