Recent Results on The Strong Perfect Graph Conjecture This work was supported in part by the National Science Foundation under Grant no. MCS78–03820.

A graph G is called perfect if for every induced subgraph H of G, the minimum number of colors needed to color the vertices of H equals the size of the largest clique in H. In the early 1960s, Claude Berge conjectured that a graph G is perfect if and only if neither G nor its complement contain an odd length chordless cycle, and this has become known as the Strong Perfect Graph Conjecture (SPGC). A circle graph is one whose vertices can be put into one-to-one correspondence with the chords of a circle such that two vertices are adjacent if and only if their corresponding chords intersect. In this work we will prove that the SPGC is true for the class of circle graphs.