Approximating coloring and maximum independent sets in 3-uniform hypergraphs

We discuss approximation algorithms for the coloring problem and the maximum independent set problem in 3-uniform hypergraphs. An algorithm for coloring 3-uniform 2-colorable hypergraphs in (O) over tilde (n(1/5)) colors is presented, improving previously known results. Also, for every fixed gamma > 1/2, we describe an algorithm that, given a 3-uniform hypergraph H on n vertices with an independent set of size gamman, finds an independent set of size <(<Omega>)over bar>(min(n, n(6 gamma -3))). For certain values of gamma we are able to improve this using the local ratio approach. The results are obtained through semidefinite programming relaxations of these optimization problems. (C) 2001 Academic Press.