On Algorithmic Methods of Analysis of Two-Colorings of Hypergraphs

Resumo

Abstract. This 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 at least k vertices of each color. In this paper, we obtain upper bounds of m_k(n) for small k and n, the exact value of m₄(8), and a lower bound for m₃(7).