On hyperedge coloring of weakly trianguled hypergraphs and well ordered hypergraphs

A well-known conjecture of Erdos, Faber and Lovasz can be stated in the following way: every loopless linear hypergraph H on n vertices can be n-edge-colored, or equivalently q(H) <= n, where q(H) is the chromatic index of H, i.e. the smallest number of colors such that intersecting hyperedges of H are colored with distinct colors. In this article we prove this assertion for Helly hypergraphs, for weakly trianguled hypergraphs, for well ordered hypergraphs and for a certain family of uniform hypergraphs. (C) 2020 Elsevier B.V. All rights reserved.