Clique tree inequalities define facets of the asymmetric traveling salesman polytope Original Research Article

This paper solves, in the affermative, the open question of whether the Grötschel-Pulleyblank clique tree inequalities define facets of the asymmetric traveling salesman polytope and its monotonization. This generalizes the corresponding result for symmetric polytopes. The proof makes use of a new recursive definition of clique tree, based on induction on the number of its “teeth” rather than of its “handles”.