Edge-coloring linear hypergraphs with medium-sized edges

Abstract

Motivated by the Erdős-Faber-Lovász (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We show that if the hyper-edge sizes are bounded between $i$ and $C_{i,\epsilon }\sqrt{n}$ inclusive, then there is a list edge coloring using $(1+\epsilon )\frac{n}{i-1}$ colors. The dependence on $n$ in the upper bound is optimal (up to the value of $C_{i,\epsilon }$).