  For any graph $G=(V,E)$, a subset $S\subseteq V$ \emph{dominates} $G$ if all
vertices are contained in the closed neighborhood of $S$, that is $N[S]=V$. The
minimum cardinality over all such $S$ is called the domination number, written
$\gamma(G)$. In 1963, V.G. Vizing conjectured that $\gamma(G \square H) \geq
\gamma(G)\gamma(H)$ where $\square$ stands for the Cartesian product of graphs.
In this note, we prove the conjecture.
