The Binested Inequalities for the Symmetric Traveling Salesman Polytope

In this paper we define a family of valid inequalities for the Symmetric Travelling Salesman Polytope which are defined on two nested sets of vertices of the graph. These inequalities generalize the comb inequalities of Chvàtal, Grötschel and Padberg, the clique tree inequalities of Grötschel and Pulleyblank, the path inequalities of Cornuéjols, Fonlupt and Naddef and the hyperstar inequalities of Fleischman. This is the largest known family of valid inequalities known so far. Facet inducing inequalities for the Symmetric Travelling Salesman Polytope contained in this class and in no other one are given proving that this is a proper generalization of the previously mentioned families.