A remark on the conjecture of Erdös, Faber and Lovász

TLDR: In this article, the celebrated Erdos, Faber and Lovasz Conjecture may be expressed as follows: any linear hypergraph on ν points has chromatic index at most ν, where ν denotes the linear intersection number and χ denotes the chromatic number of the graph.

Abstract: The celebrated Erdos, Faber and Lovasz Conjecture may be stated as follows: Any linear hypergraph on ν points has chromatic index at most ν We show that the conjecture is equivalent to the following assumption: For any graph \(\chi(G) \leq \nu(G)\), where ν(G) denotes the linear intersection number and χ(G) denotes the chromatic number of G As we will see \(\chi(G) + \chi(\bar{G}) \leq \nu(G)+ \nu(\overline{G})\) for any graph G = (V, E), where \((\overline{G})\) denotes the complement of G Hence, at least G or \(\overline{G}\) fulfills the conjecture