On a generalization of the Erdos-Lovasz problem

We study a generalization of the classical Erdos-Lovasz problem dealing with coloring nonuniform hypergraphs. Let H = (V,E) be an arbitrary hypergraph whose minimum edge size is n and its girth is at least 4. We obtain a new sufficient condition for r-colorability of the hypergraph H in terms of some bounds on the function fr(H) =∑eϵЕr1-ӀeӀ.