  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 $PSB (n)$ 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
$PSB (n)$ is the graph whose vertex set is the vertex set of $PSB (n)$ and the
edge set is the set of geometric edges or one-dimensional faces of $PSB (n)$.
The main result of the paper is a necessary and sufficient condition for vertex
adjacencies in the skeleton of the polytope $PSB (n)$ that can be verified in
polynomial time.
