The Erdos-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 subset of V (G) such that vertical bar A vertical bar, vertical bar B vertical bar >= epsilon n, and A is either complete or anticomplete to B. This proves the analog of the Erdos-Hajnal conjecture for the class of graphs with no pivot-minor isomorphic to Ck.