On the facial structure of Symmetric and Graphical Traveling Salesman Polyhedra

Abstract The Symmetric Traveling Salesman Polytope S for a fixed number n of cities is a face of the corresponding Graphical Traveling Salesman Polyhedron P . This has been used to study facets of S using P as a tool. In this paper, we study the operation of “rotating” (or “lifting”) valid inequalities for S to obtain a valid inequalities for P . As an application, we describe a surprising relationship between (a) the parsimonious property of relaxations of the Symmetric Traveling Salesman Polytope and (b) a connectivity property of the ridge graph of the Graphical Traveling Salesman Polyhedron.

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