3 research outputs found
On vertex adjacencies in the polytope of pyramidal tours with step-backs
We consider the traveling salesperson problem in a directed graph. The
pyramidal tours with step-backs are a special class of Hamiltonian cycles for
which the traveling salesperson problem is solved by dynamic programming in
polynomial time. The polytope of pyramidal tours with step-backs is
defined as the convex hull of the characteristic vectors of all possible
pyramidal tours with step-backs in a complete directed graph. The skeleton of
is the graph whose vertex set is the vertex set of and the
edge set is the set of geometric edges or one-dimensional faces of .
The main result of the paper is a necessary and sufficient condition for vertex
adjacencies in the skeleton of the polytope that can be verified in
polynomial time.Comment: in Englis