Approximating Maximum Independent Sets in Uniform Hypergraphs

We consider the problem of approximating the independence number and the chromatic number of k-uniform hypergraphs on n vertices. For xed integers k 2, we obtain for both problems that one can achieve in polynomial time approximation ratios of at most O(n=(log 1) n)2). This extends results of Boppana and Halld orsson [5] who showed for the graph case that an approximation ratio of O(n=(logn)) can be achieved in polynomial time. On the other hand, assuming NP 6= ZPP , one cannot obtain in polynomial time for the independence number and the chromatic number of k-uniform hypergraphs an approximation ratio of n for xed > 0.