This article is cited in 2 papers

On some generalizations of the property B problem of an $n$-uniform hypergraph

Yu. A. Demidovich

Moscow Institute of Physics and Technology, Moscow, Russia

Abstract: The extremal problem of hypergraph colorings related to the Erdős–Hajnal property $B$-problem is considered. Let $k$ be a natural number. The problem is to find the value of $m_k(n)$ equal to the minimal number of edges in an $n$-uniform hypergraph that does not admit $2$-colorings of the vertex set such that every edge of the hypergraph contains at least $k$ vertices of each color. In this paper, we obtain new lower bounds for $m_k(n)$.

UDC: 519.218

 English version: Journal of Mathematical Sciences (New York), 2022, 262:4, 457–475