Partial monotonizations of Hamiltonian cycle polytopes: dimensions and diameters Original Research Article

In this paper we study partial monotonizations and level polytopes of the Hamiltonian Cycle Polytope, also called the symmetric Traveling Salesman Polytope. The kth Level Polytope is the convex hull of the characteristic vectors corresponding to sets of k edges in Kn that can be extended to Hamiltonian cycles (n⩾3). For 0⩽α⩽k, the α-monotonization of the kth Level Polytope is the convex hull of the characteristic vectors corresponding to sets of at least α and at most k edges in Kn that can be extended to Hamiltonian cycles (n⩾3). It is shown that for α