A note on the relationship between the Graphical Traveling Salesman   Polyhedron, the Symmetric Traveling Salesman Polytope, and the Metric Cone
  In this short communication, we observe that the Graphical Traveling Salesman Polyhedron is the intersection of the positive orthant with the Minkowski sum of the Symmetric Traveling Salesman Polytope and the polar of the metric cone. This follows almost trivially from known facts. There are two reasons why we find this observation worth communicating none-the-less: It is very surprising; it helps to understand the relationship between these two important families of polyhedra. 
Dirk Oliver Theis