A homogeneous pair is related to a modular decomposition of a graph. It is a partition of the graph into three subsets "V"1, "V"2, and "V"3 such that "V"1 and "V"2 together contain at least three vertices, "V"3 contains at least two vertices, and for each vertex "v" in "V"3 and each "i" in {1,2} either "v" is adjacent to all vertices in "V""i" or to none of them. It is not possible for a minimally imperfect graph to have a homogeneous pair. Subsequent to the proof of the strong perfect graph conjecture, simplified it by showing that homogeneous pairs could be eliminated from the set of decompositions used in the proof.