On the Degree, Size, and Chromatic Index of a Uniform Hypergraph

Let H be a k-uniform hypergraph in which no two edges share more than t common vertices, and let D denote the maximum degree of a vertex of H. We conjecture that for every > 0, if D is sufficiently large as a function of t, k and , then the chromatic index of H is at most (t − 1 + 1/t + )D. We prove this conjecture for the special case of intersecting hypergraphs in the following stronger form: If H is an intersecting k-uniform hypergraph in which no two edges share more than t common vertices, and D is the maximum degree of a vertex of H, where D is sufficiently large as a function of k, then H has at most (t− 1 + 1/t)D edges.