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Keywords:

  • multipartite graphs;
  • hypergraphs;
  • list coloring;
  • separation;
  • 05C15

Abstract

For a hypergraph G and a positive integer s, let inline image be the minimum value of l such that G is L-colorable from every list L with inline image for each inline image and inline image for all inline image. This parameter was studied by Kratochvíl, Tuza, and Voigt for various kinds of graphs. Using randomized constructions we find the asymptotics of inline image for balanced complete multipartite graphs and for complete k-partite k-uniform hypergraphs.