A pair of vertices of a graph is called an -critical pair if , where denotes the graph obtained by adding the edge to and is the clique number of . The -critical pairs are never edges in . A maximal stable set of is called a forced color class of if meets every -clique of , and -critical pairs within form a connected graph.

In 1993, G. Bacsó conjectured that if is a uniquely -colorable perfect graph, then has at least one forced color class. This conjecture is called the bold conjecture, and implies the strong perfect graph theorem. However, a counterexample of the conjecture was subsequently found by Sakuma (1997).