Thomas Murff, Xerxes D. Arsiwalla

This work studies upper bounds on the chromatic index of linear, loopless hypergraphs. The first bound is derived using a color-preserving group acting on a properly and minimally edge-colored hypergraph, where the group’s orbits create a finer partition of the coloring. This provides an upper bound on the chromatic index. The following results examine combinatorial properties of hypergraph coloring and outline a possible approach to the Berge–Füredi conjecture, linking the chromatic index to the maximum degree of the associated graph plus one. Three sufficient conditions are also identified for the conjecture to hold, involving the Helly property for hypergraphs.