Faces with large diameter on the symmetric traveling salesman polytope

This paper deals with the symmetric traveling salesman polytope and contains three main theorems. The first one gives a new characterization of (non)adjacency. Based on this characterization a new upper bound for the diameter of the symmetric traveling salesman polytope (conjectured to be 2 by M. Grötschel and M.W. Padberg) is given in the third theorem. D. Hausman has proved that (non)adjacency of two vertices of the symmetric traveling salesman polytope can be tested on a face, induced by these two vertices. The second theorem shows that some of these faces have a large diameter and therefore cannot be used in proving the above conjecture.