Near optimal list colorings

We show that a simple variant of a naive coloring procedure can be used to list color the edges of a k-uniform linear hypergraph of maximum degree Δ provided every vertex has a list of at least Δ+c(log Δ)4Δ1−(1/k) available colors (where c is a constant which depends on k). We can extend this to color hypergraphs of maximum codegree o(Δ) with Δ+o(Δ) colors. This improves earlier results of Kahn and our techniques are quite similar. We also develop efficient algorithms to obtain such colorings when Δ is constant. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17: 376–402, 2000

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