Chromatic index of simple hypergraphs (Q2005680)

The authors consider the problem of edge coloring of simple hypergraphs. There is a very well-known conjecture given independly by \textit{C. Berge} [in: Combinatorial mathematics, Proc. 3rd Int. Conf., New York/ NY (USA) 1985, Ann. N. Y. Acad. Sci. 555, 40--44 (1989; Zbl 0726.05055)] and \textit{Z. Füredi} [Graphs Comb. 2, 89--92 (1986; Zbl 0589.05036)]. It says that \(\chi^\prime(H)\leq \Delta(H)+1\) for any simple hypergraph \(H\). The authors prove this conjecture for simple hypergraphs of degree at most 5. Moreover, they give a new upper bound on the chromatic index of the hypergraph \(H\), namely \(\chi^\prime(H)\leq \frac{7}{4}\Delta(H) - 1\). The paper gives a very nice contribution to the problem of hyperedge coloring.