A skew partition is a partition of a graph's vertices into two subsets, one of which induces a disconnected subgraph and the other of which has a disconnected complement; had conjectured that no minimal counterexample to the strong perfect graph conjecture could have a skew partition. Chudnovsky et al. introduced some technical constraints on skew partitions, and were able to show that Chvátal's conjecture is true for the resulting "balanced skew partitions". The full conjecture is a corollary of the strong perfect graph theorem.