Traveling salesman polytopes and cut polytopes. Affine reducibility

Abstract

Let STSPm be the TSP (traveling salesman polytope) for m cities, and let CUTn be the cut polytope of the complete n-vertex graph. It is shown that CUTn is affinely equivalent to some face of the polytope STSPm with m = (2n−2)(2n−3). On the other hand, STSPm is shown to be an affine image of some face of the polytope CUTn with n = (m − 1)2 + 1.