Irredundance perfect graphs

Abstract The domination number γ ( G ) and the irredundance number ir ( G ) of a graph G have been considered by many authors. It is well known that ir ( G ) ⩽ γ ( G ) holds for all graphs G . In this paper we investigate the concept of irredundance perfect graphs which deals with those graphs that have all their induced subgraphs H satisfying ir ( H ) = γ ( H ). We give a characterization of those graphs G for which ir ( H ) = γ ( H ) for every induced subgraph H of G with ir ( H ) = 2 in terms of 30 forbidden induced subgraphs. A sufficient condition for ir ( G ) = γ ( G ) for a graph G with ir ( G ) ⩽ 4 is given in terms of three forbidden subgraphs. This result strengthens a conjecture due to Favaron (1986) which states that if a graph G does not contain these three forbidden subgraphs, then ir ( G ) = γ ( G ).

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