The List-Chromatic Number of Complete Multipartite Hypergraphs and Multiple Covers by Independent Sets

This paper deals with list colorings of uniform hypergraphs. Let H ( m, r, k ) be the complete r -partite k -uniform hypergraph with parts of equal size m in which each edge contains exactly one vertex from some k ≤ r parts. Using results on multiple covers by independent sets, we establish that, for fixed k and r , the list-chromatic number of H ( m, r, k ) is (1 + o (1)) log r/ ( r−k +1) ( m ) as m → ∞.