Equitable Coloring of -Uniform Hypergraphs

Let be a k-uniform hypergraph with vertices. A is a partition of the vertices into parts, such that each edge of intersects each part. A strong r-coloring is called if the size of each part is or . We prove that for all ≥ 1, if the maximum degree of satisfies then has an equitable coloring with parts. In particular, every k-uniform hypergraph with maximum degree () has an equitable coloring with parts. The result is asymptotically tight. The proof uses a double application of the non-symmetric version of the Lovász Local Lemma