This article is cited in 3 papers

On balanced colorings of hypergraphs

A. P. Rozovskaya, M. V. Titova, D. A. Shabanov

M. V. Lomonosov Moscow State University

Abstract: The paper deals with an extremal problem concerning hypergraph colorings. Let $k$ be an integer. The problem is to find the value $m_k(n)$ equal to the minimum number of edges in an $n$-uniform hypergraph not admitting two-colorings of the vertex set such that every edge of the hypergraph contains $k$ vertices of each color. In this paper, we obtain the exact values of $m_2(5)$ and $m_2(4)$, and the upper bounds for $m_3(7)$ and $m_4(9)$.

UDC: 519.179.1+519.157

 English version: Journal of Mathematical Sciences (New York), 2010, 169:5, 654–670

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