Upper bound in the Erdős-Hajnal problem of hypergraph coloring (Q1947784)

This paper deals with the quantity \(m_k (n)\), the least number of edges of an \(n\)-homogeneous hypergraph whose vertices cannot be two colored in such a way that every edge contains at least \(k\) vertices of each color class. The bound for \(m_ k(n)\) obtained in [\textit{D. A. Shabanov}, Izv. Math. 71, No. 6, 1253--1290 (2007); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 71, No. 6, 183--222 (2007; Zbl 1247.05116)] is obtained here under weaker assumptions on \(k\).