On general two-colorings of uniform hypergraphs

A study was conducted to report the well-known extremal problem on colorings of uniform hypergraphs. A hypergraph was defined as a pair of sets H = (V, E), where V was a finite set, called the vertex set of the hypergraph, and E was a family of subsets of V, called the edge set of the hypergraph. A hypergraph was also considered to be n-uniform when each of its edges contains precisely n vertices. A classical extremal problem of hypergraph theory was the problem about the property B of hypergraphs. The proof of Theorem 1 was based on a criterion for a hypergraph with property Bk that was formulated in Theorem 2.