A new integer programming formulation of the graphical traveling salesman problem

In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost c ij of traveling from city i to city j , which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of polynomial-sized constraints while addressing an open question proposed by Denis Naddef. We generalize one of these classes, and present promising preliminary computational results.