The Erdos-Faber-Lovasz conjecture for weakly dense hypergraphs

Abstract

Generalizing the concept of dense hypergraph, we say that a hypergraph is weakly dense, if no k in the half-open interval [2,sqrt(n)) is the degree of more than k^2 vertices. In our main result, we prove the famous Erdos-Faber-Lovasz conjecture when the hypergraph is weakly dense.

graph coloring; combinatorics