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

Let H be ak-uniform hypergraph in which no two edges share more thantcommon vertices, and letDdenote the maximum degree of a vertex of H. We conjecture that for everyε>0, ifDis sufficiently large as a function oft, k, andε, then the chromatic index of H is at most (t−1+1/t+ε) D. We prove this conjecture for the special case of intersecting hypergraphs in the following stronger form: If H is an intersectingk-uniform hypergraph in which no two edges share more thantcommon vertices andDis the maximum degree of a vertex of H, whereDis sufficiently large as a function ofk, then H has at most (t−1+1/t) Dedges.