Panchromatic equitable colorings of uniform simple hypergraphs

The article deals with a problem of panchromatic equitable colorings of uniform simple hypergraphs. Let H = (V, E) be a hypergraph, a vertex r-coloring of V is called panchromatic if each of the edges of E meets every of r colors. A vertex r-coloring is said to be a panchromatic equitable one if it is panchromatic and the cardinalities of every two color classes differ at most by one. We prove a new bound for the maximal vertex degree that provides the existence of a panchromatic equitable 3-coloring of a simple n-uniform hypergraph.