On the existence of graphs with prescribed coloring parameters

Abstract The pseudoachromatic number ψ(G) of a graph G is the maximum size of a vertex partition of G (where the sets of the partition may or may not be independent) such that between any two distinct parts, there is at least one edge of G . Here, we prove that if 2⩽a⩽b⩽c , then there exists a graph G with chromatic number a , achromatic number b and pseudoachromatic number c .