The Strong Perfect Graph Conjecture for Planar Graphs
Alan C. Tucker · Canadian Journal of Mathematics · 1973
A graph G is called γ-perfect if ƛ (H) = γ (H) for every vertex-generated subgraph H of G. Here, ƛ (H) is the clique number of H (the size of the largest clique of H) and γ (H) is the chromatic number of H (the minimum number of independent sets of vertices that cover all vertices of H). A graph G is called α-perfect if α (H) = θ(H) for every vertex-generated subgraph H of G, where α (H) is the stability number of H (the size of the largest independent set of H) and θ(H) is the partition number of H (the minimum number of cliques that cover all vertices of H).