A perfect graph is a graph G such that for every induced subgraph of G, the clique number equals the chromatic number, i.e., ω(G) = χ(G). A graph that is not a perfect graph is called an imperfect graph. A graph for which ω(G) = χ(G) (without any requirement that this condition also hold on induced subgraphs) is called a weakly perfect graph. All perfect graphs are therefore weakly perfect by definition.

chordal graph | chromatic number | clique | imperfect graph | induced subgraph | odd chordless cycle | perfect graph theorem | perfect matching | Shannon capacity | strongly perfect graph | strong perfect graph theorem | weakly perfect graph