The monotonic diameter of traveling salesman polytopes

The monotonic diameter of the polytopes arising in the asymmetric and the symmetric traveling salesman problem (TSP) are obtained. For the asymmetric TSP polytope associated with the complete directed graph on n nodes, the monotonic diameter is shown to be exactly right |n/3|, for all n greater than or equal to 3. For symmetric TSP polytope associated with the complete undirected graph on n nodes, the monotonic diameter is shown to be exactly |n/2| − 1, for all n greater than or equal to 3, except for n = 5, in which case it is |n/2|.