Equitable colorings of hypergraphs with few edges
The paper deals with an extremal problem concerning equitable colorings of uniform hypergraphs. Recall that a vertex coloring of a hypergraph is called proper if there are no monochromatic edges under this coloring. A hypergraph is said to be equitably r-colorable if there is a proper coloring with r colors such that the sizes of any two color classes differ by at most one. In the present paper we prove a new lower for the number of edges for an n-uniform hypergraph taht does not admit an equitable r-coloring.