Perfect Graphs were defined by Claude Berge in 1961. Since that time this class of graphs has been intensely studied. Much of the work has been directed towards proving Berge's Strong and Weak Perfect Graph Conjectures. L. Lovász finally demonstrated the Weak Perfect Graph Conjecture in 1972. Vaśek Chvátal, in 1982, proposed the Semi-Strong Perfect Graph Conjecture which falls between these two conjectures. This conjecture suggests that the perfection of a graph depends solely on the way that the chordless paths with three edges are distributed within the graph. This paper contains a proof of Chvátal's conjecture.
