Four NP-hard optimization problems on graphs are studied: The vertex separator problem, the edge separator problem, the … maximum clique problem, and the maximum independent set problem. We show that the vertex separator problem is equivalent to a … along the edges of the feasible set. An algorithm is given which exploits the continuous formulation of the vertex separator …

Given G = (V, E) a connected undirected graph and a positive integer β(|V|), the vertex separator problem is to find a … minimum. In this paper we consider the vertex separator problem from a polyhedral point of view. We introduce new classes of …