Optimum Path Packing on Wheels :

We show that, given a wheel with nonnegative edge lengths and pairs of terminals located on the wheel's outer cycle such that no two terminal pairs cross, then a path packing, i. e., a collection of edge disjoint paths connecting the given terminal pairs, of minimum length can be found in strongly polynomial time. Moreover, we exhibit for this case a system of linear inequalities that provides a complete and nonredundant description of the path packing polytope, which is the convex hull of all incidence vectors of path packings and their supersets.