  We prove that any total boolean function of rank $r$ can be computed by a
deterministic communication protocol of complexity $O(\sqrt{r} \cdot \log(r))$.
Equivalently, any graph whose adjacency matrix has rank $r$ has chromatic
number at most $2^{O(\sqrt{r} \cdot \log(r))}$. This gives a nearly quadratic
improvement in the dependence on the rank over previous results.
