Reconnaissance des graphes de cordes

Abstract

A simple graph G = ( V, E) is a circle graph if one can associate to G a diagram C( V), consisting of a circle C together with a set V of chords of C, in such way that adjacency of vertices corresponds to crossing of corresponding chords. An orientation of a chord x of C( V) allows us to define the left side and the right side of x. The relation: “the initial end of the chord x is on the left side of the chord y” associated to an arbiratry orientation of the chords of C( V) gives an orientation of the edges of G and a double labelling of the edges of the complementary graph G ̄ . We study the combinatorial relationships between such an orientation and such a double labelling. We derive from this a characterization of circle graphs which yields a polynomial time recognition algorithm.