Construction of Hamiltonian paths in graphs of permutation polyhedra

The problem of finding an extremum of a linear function over a permutation set is considered. The polyhedron of admissible values of this function over permutations is constructed. The constructed graph is shown to be partially ordered with respect to the transposition of two elements of a permutation. Based on this property, a method is proposed for the construction of a Hamiltonian path in the graph corresponding to the permutation set for n=4.