Approximate coloring of uniform hypergraphs

We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of finding the exact value of the chromatic number of a hypergraph is known to be NP-hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r 3 it is impossible to approximate in polynomial time the chromatic number of r-uniform hypergraphs on n vertices within a factor n1− for any > 0, unless NP ⊆ ZPP. On the positive side, improving a result of Hofmeister and Lefmann, we present an approximation algorithm for coloring r-uniform hypergraphs on n vertices, whose performance ratio is O(n(log logn)2/(logn)2).  2003 Elsevier Inc. All rights reserved.