Vizing's conjecture: a two-thirds bound for claw-free graphs
  We show that for any claw-free graph $G$ and any graph $H$, $\gamma(G\square H)\geq \frac{2}{3}\gamma(G)\gamma(H)$, where $\gamma(G)$ is the domination number of $G$. 
Elliot Krop
math.CO