Around Erdos-Lovasz problem on colorings of non-uniform hypergraphs

The work deals with combinatorial problems concerning colorings of non-uniform hypergraphs. Let H = (V, E) be a hypergraph with minimum edge-cardinality n. We show that if H is a simple hypergraph (i.e. every two distinct edges have at most one common vertex) and (e is an element of E)Sigma r(1-vertical bar e vertical bar) <= c root n, for some absolute constant c > 0, then H is r-colorable. We also obtain a stronger result for triangle-free simple hypergraphs by proving that if H is a simple triangle-free hypergraph and (e is an element of E)Sigma r(1-vertical bar e vertical bar) <= c . n, for some absolute constant c > 0, then H is r-colorable. (C) 2015 Elsevier B.V. All rights reserved.