Semidefinite Programs and Combinatorial Optimization

Abstract

ed by G k . We denote by ff(G) the maximum number of independent points (the maximum size of a stable set) in graph G = (V; E). Thus ff(G k ) is the maximum number of words of length n, composed of elements of V , so that for every two words there is at least one i (1 i k) such that the i-th letters are different and non-adjacent in G. The Stable Set Problem is the problem of finding ff(G). Proposition 1.1 The Stable Set Problem is NP-hard. In fact, it is NP-hard to determine ff(G) with a relative error less than n 1=10 , where n = jV j.