Some properties of the skeleton of the pyramidal tours polytope

We consider the skeleton of the pyramidal tours polytope PYR(n) that is defined as the convex hull of characteristic vectors of all pyramidal tours in the complete graph Kn. We describe necessary and sufficient condition for the adjacency of vertices of PYR(n) polytope. Based on that, we establish that the diameter of PYR(n) skeleton equals 2, and the asymptotically exact estimate of PYR(n) skeleton's clique number is Θ(n2). This value characterizes the time complexity in a broad class of algorithms based on linear comparisons.