The ωψ-perfection of graphs

In this paper we study a natural generalization for the perfection of graphs to other interesting parameters related with colorations. This generalization was introduced partially by Christen and Selkow in 1979 and Yegnanarayanan in 2001.Let a,b∈{ω,χ,Γ,α,ψ} where ω is the clique number, χ is the chromatic number, Γ is the Grundy number, α is the achromatic number and ψ is the pseudoachromatic number. A graph G is ab-perfect if for every induced subgraph H, a(H)=b(H). In this work we characterize the ωψ-perfect graphs.