Complete Multi-partite Cutsets in Minimal Imperfect Graphs

We show that a minimal imperfect graph G cannot contain a cutset C which induces a complete multi-partite graph unless C is a stable set and G is an odd hole. This generalizes a result of Tucker, who proved that the only minimal imperfect graphs containing stable cutsets are the odd holes. It is also a special case of a conjecture of Chvلtal.