2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142512In 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.21 pages, 4 figuresDiscrete MathematicsG.2.2text