Worst-case comparison of valid inequalities for the TSP

The paper considers most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst-case imporvement resulting from their addition to the subtour polyhedron. For example, it shows that the comb inequalities cannot improve the subtour bound by a factor greater than The corresponding factor for the class of clique tree inequalities is , while it is for the path configuration inequalities.