ИСТИНА

Abstract The paper is devoted to the combinatorial problem concerning equitable colorings of non-uniform simple hypergraphs. Let H = (V,E) be a hypergraph, a coloring with r colors of its vertex set V is called equitable if it is proper (i.e. none of the edges is monochromatic) and the cardinalities of the color classes differ by at most one. We show that if H is a simple hypergraph with minimum edge-cardinality n and e∈E r1−|e| c √n, for some absolute constant c > 0, then H has an equitable r-coloring. Keywords: Hypergraphs, colourings, Property B.