Bounds on Erd{ő}s - Faber - Lovász Conjecture - the Uniform and Regular Cases

Abstract

We consider the Erd{ő}s - Faber - Lovász (EFL) conjecture for hypergraphs. This paper gives an upper bound for the chromatic number of $r$ regular linear hypergraphs $\text{H}$ of size $n$. If $r\ge 4$, $\chi (\text{H})\le 1.181n$ and if $r=3$, $\chi (\text{H})\le 1.281n$

5 pages