On counting independent sets in sparse graphs

We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree /spl Delta/. The first result implies that the Monte-Carlo Markov chain technique is likely to fail if /spl Delta//spl ges/6. The second shows that no fully polynomial randomized approximation scheme can exist for /spl Delta//spl ges/25, unless P=NP under randomized reductions.