On hyperedge coloring of weakly trianguled hypergraphs and well ordered hypergraphs
Résumé
A well-known conjecture of Erdős, Faber and Lovász 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.
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