Let H be the 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 epsilon > 0, if D is sufficiently large as a function of t, k, and epsilon, then the chromatic index of H is at most (t - 1 + 1/t + epsilon) 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. (C) 1997 Academic Press
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