A new integer programming formulation of the graphical traveling salesman problem

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