Bounds on Erd{\H{o}}s - Faber - Lov\'{a}sz Conjecture - the Uniform and Regular Cases

Abstract

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