The Erdos-Hajnal conjecture for graphs with no five-cycle

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Sophie Spirkl, University of Waterloo

The Erdos-Hajnal conjecture states that for every graph H there exists c > 0 such that every n-vertex graph G either contains H as an induced subgraph, or has a clique or stable set of size at least n^c. I will talk about a proof of this conjecture for the case H = 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.