Abstract
The vertices of the skeleton of the symmetric Traveling Salesman Polytope are the characteristic vectors corresponding to the Hamiltonian tours in the complete graph K n with n ⩾3, and the edges of this skeleton are the 1-faces of the polytope. It is shown that this skeleton contains a Hamiltonian tour such that the Hamiltonian cycles in K n corresponding to two successive vertices differ in a single interchange, i.e., the interchange graph corresponding to the TSP-polytope is Hamiltonian. It is also shown that the skeleton can be covered by 1 2 ( n −2)! cliques, and has diameter at most n −3.
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