Perfect graphs

Perfect graphs are a special class of graphs in combinatorial optimization and graph theory. A graph \( G \) is called perfect if for every induced subgraph \( H \) of \( G \), the size of the largest clique in \( H \) (denoted as \( \omega(H) \)) is equal to the size of the smallest vertex coloring of \( H \) (denoted as \( \chi(H) \)).