The Erdős-Hajnal property for graphs with no fixed cycle as a pivot-minor

Abstract

We prove that for every integer $k$, there exists $\epsilon >0$ such that for every n-vertex graph $G$ with no pivot-minor isomorphic to $C_k$, there exist disjoint sets $A,B\subseteq V(G)$ such that $|A|,|B|\ge \epsilon n$, and $A$ is either complete or anticomplete to $B$. This proves the analog of the Erdős-Hajnal conjecture for the class of graphs with no pivot-minor isomorphic to $C_k$.

13 pages, 4 figures