The recently announced Strong Perfect Graph Theorem states that the class of
perfect graphs coincides with the class of graphs containing no induced
odd cycle of length at least 5 or the complement of such a cycle. A
graph in this second class is called Berge. A bull is a graph with five
vertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph is
bull-reducible if no vertex is in two bulls. In this paper we give a
simple proof that every bull-reducible Berge graph is perfect. Although
this result follows directly from the Strong Perfect Graph Theorem, our proof
leads to a recognition algorithm for this new class of perfect graphs whose
complexity, O(n6), is much lower than that announced for perfect graphs.