Approximate coloring of uniform

We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of nding 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, we present an approximation algorithm for coloring r-uniform hypergraphs on n vertices, whose performance ratio is O(n(log log n)2=(log n)2). We also describe an algorithm for coloring 3-uniform 2-colorable hypergraphs on n vertices in ~ O(n9=41) colors, thus improving previous results of Chen and Frieze and of Kelsen, Mahajan and Ramesh.