Common domination perfect graphs

Abstract

A dominating set in a graph G is a set S of vertices such that every vertex that does not belong to S is adjacent to a vertex in S. The domination number γ(G) of G is the minimum cardinality of a dominating set of G. The common independence number α c (G) of G is the greatest integer r such that every vertex of G belongs to some independent set of cardinality at least r. The common independence number is squeezed between the independent domination number i(G) and the independence numberWe define a graph G as common domination perfect if γ(H) = α c (H) for every induced subgraph H of G. We provide a characterization of common domination perfect graphs in terms of ten forbidden induced subgraphs.