  In an undirected connected graph G=(V,E), the vertex separator problem (VSP)
asks for a partition of V into nonempty subsets A, B, C such that |C| is
minimized such that there is no edge between A and B, and sizes of A and B are
similar. This paper presents a polyhedral approach of the (VSP), introducing
new efficient valid inequalities and providing computational tests and results.
