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            <title xml:lang="en">An exact algorithm for solving the vertex separator problem</title>
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              <p>Given G = (V, E) a connected undirected graph and a positive integer β(|V |), the vertex separator problem is to find a partition of V into no-empty three classes A, B, C such that there is no edge between A and B, max{|A|, |B|} ≤ β(|V |) and |C| is minimum. In this paper we consider the vertex separator problem from a polyhedral point of view. We introduce new classes of valid inequalities for the associated polyhedron. Using a natural lower bound for the optimal solution, we present successful computational experiments.</p>
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