Choosability with separation of complete multipartite graphs and hypergraphs
Abstract
For a hypergraph G and a positive integer s, let (G,s) be the minimum value of l such that G is L-colorable from every list L with |L(v)|=l for each v∈ V(G) and |L(u) L(v)|≤ s for all u, v∈ e∈ E(G). This parameter was studied by Kratochv\'il, Tuza and Voigt for various kinds of graphs. Using randomized constructions we find the asymptotics of (G,s) for balanced complete multipartite graphs and for complete k-partite k-uniform hypergraphs.
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