String graphs have the Erd\H{o}s-Hajnal property

24 Feb 2020 · Tomon István ·

A string graph is the intersection graph of curves in the plane. We prove that there exists an absolute constant $c>0$ such that if $G$ is a string graph on $n$ vertices, then $G$ contains either a clique or an independent set of size at least $n^{c}$.