Forbidden Graphs and Irredundant Perfect Graphs

Abstract

The domination number $\gamma (G)$ and the irredundance number $ir(G)$ of a graph $G$ have been considered by many authors. It is well known that $ir(G)\le \gamma (G)$ holds for all graphs $G$. In this paper we determine all pairs of connected graphs $(X,Y)$ such that every graph $G$ containing neither $X$ nor $Y$ as an induced subgraph satisfies $ir(G)=\gamma (G)$.