Edge‐coloring linear hypergraphs with medium‐sized edges. Issue 1 (1st March 2019) - Faber, Vance; Harris, David G.
Abstract : Motivated by the Erdos̋‐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, ϵ n inclusive, then there is a list edge coloring using ( 1 + ϵ ) n i − 1 colors. The dependence on n in the upper bound is optimal (up to the value of C i, ϵ ).