Abstract
Berge's well known SPGC (Strong Perfect Graph Conjecture) 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. We prove that every bull-reducible Berge graph is perfect and we exhibit a polynomial-time recognition algorithm for bull-reducible Berge graphs.
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