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

Published 21 Jun 2018 in math.CO | (1806.08154v2)

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 $r=3$, $\chi(\textbf{H}) \le 1.281n$

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