A note on the Erdős-Hajnal property for stable graphs

Abstract

In this short note we provide a relatively simple proof of the Erdős-Hajnal conjecture for families of finite (hyper-)graphs without the $k$-order property. It was originally proved by M. Malliaris and S. Shelah in "Regularity lemmas for stable graphs", Transactions AMS, 366, 2014, 1551-1585.

v2: 6 pages, some minor errors are corrected, and some details are added to the proof