  A well-known conjecture of Vizing is that $\gamma(G \square H) \ge
\gamma(G)\gamma(H)$ for any pair of graphs $G, H$, where $\gamma$ is the
domination number and $G \square H$ is the Cartesian product of $G$ and $H$.
Suen and Tarr, improving a result of Clark and Suen, showed $\gamma(G \square
H) \ge \frac{1}{2}\gamma(G)\gamma(H) + \frac{1}{2}\min(\gamma(G),\gamma(H))$.
We further improve their result by showing $\gamma(G \square H) \ge
\frac{1}{2}\gamma(G)\gamma(H) + \frac{1}{2}\max(\gamma(G),\gamma(H)).$
