The Erdos-Faber-Lovasz conjecture for weakly dense hypergraphs

TL;DR

This paper proves the Erdos-Faber-Lovasz conjecture for a new class of hypergraphs called weakly dense hypergraphs, extending the understanding of hypergraph coloring and structure.

Contribution

It introduces the concept of weakly dense hypergraphs and proves the Erdos-Faber-Lovasz conjecture within this class, a significant extension of previous results.

Findings

Erdos-Faber-Lovasz conjecture holds for weakly dense hypergraphs

Weakly dense hypergraphs have bounded degrees in specific intervals

The paper extends hypergraph coloring theory to new hypergraph classes

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.