  We prove a conjecture of Kim and Oum that every proper pivot-minor-closed
class of graphs has the strong Erd\H{o}s-Hajnal property. More precisely, for
every graph $H$, there exists $\epsilon > 0$ such that every $n$-vertex graph
with no pivot-minor isomorphic to $H$ contains two sets $A, B$ of vertices such
that $|A|, |B| \ge \epsilon n$ and $A$ is complete or anticomplete to $B$.
