  Let $\gamma(G)$ and $\beta(G)$ denote the domination number and the covering
number of a graph $G$, respectively. A connected non-trivial graph $G$ is said
to be $\gamma\beta$-{perfect} if $\gamma(H)=\beta(H)$ for every non-trivial
induced connected subgraph $H$ of $G$. In this note we present an elementary
proof of a characterization of the $\gamma\beta$-perfect graphs.
