New lower bound for the minimal number of edges of simple uniform hypergraph without the property $B_k$

Yu. A. Demidovich

Moscow Institute of Physics and Technology (National Research University)

Abstract: A hypergraph $H=(V,E)$ has the property $B_k$ if there exists an assignment of two colors to $V$ such that each edge contains at least $k$ vertices of each color. A hypergraph is called simple if every two edges of it have at most one common vertex. We obtain a new lower bound for the minimal number of edges of $n$-uniform simple hypergraph without the property $B_k$.

Keywords: simple hypergraphs, colorings of hypergraphs, property $B$.

UDC: 519.174, 519.179.1

Received: 30.07.2020

DOI: 10.4213/dm1621

 English version: Discrete Mathematics and Applications, 2022, 32:3, 155–176

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