Affine hull of the 𝑚-tour polytope

Source abstract

This paper studies the problem commonly known as the multiple traveling salesmen problem. Given salesmen and cities, each city must be visited by exactly one salesman. All salesmen must be used, and each tour must start and end at the same city. The distances between every pair of cities are given. The task is to find pairwise edge-disjoint tours of minimum total length. We investigate the polytope associated with the set of all𝑚-tours. The affine hull of this polytope is obtained, and its dimension is found.