Chudnovsky et al. showed that every perfect graph either belongs to one of five basic classes of perfect graphs .
Graph has one of four types of decomposition into simpler graphs , one of which is a skew partition .
Chudnovsky et al. showed that every perfect graph either belongs to one of five basic classes of perfect graphs , or it has one of four types of decomposition into simpler graphs , one of which is a skew partition .