Abstract
Vertices x and y in the same graph are called partners if there is a set S of three vertices such that both S ∪ { x} and S ∪ { y} induce a chordless path. If the vertices of G can be distributed into two disjoint classes in such a way that every two partners belong to the same class and that each class induces in G a perfect graph then G is perfect. This theorem generalizes two theorems that were proved before, one by Chvátal and Hoàng, and the other by Hoàng alone.
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