The Erdős-Hajnal conjecture for the five-cycle

Abstract:

The Erdős-Hajnal conjecture states that for every graph HH there exists c>0c>0 such that every nn-vertex graph GG either contains HH as an induced subgraph, or has a clique or stable set of size at least nc.nc. I will talk about a proof of this conjecture for the case H=C5H=C5 (a five-cycle), and related results. The proof is based on an extension of a lemma about bipartite graphs due to Pach and Tomon.

This is joint work with Maria Chudnovsky, Alex Scott, and Paul Seymour.