New facets of the STS polytope generated from known facets of the ATS polytope

While it was known for a long time how to transform an asymmetric traveling salesman problem on the complete graph with n vertices into a symmetric traveling salesman problem on an incomplete graph with 2n vertices, no method was available until recently for using this correspondence to derive facets of the symmetric traveling salesman polytope from facets of the asymmetric one. In this paper we develop a procedure for accomplishing this task, and use it to obtain several classes of new facet defining inequalities for the symmetric polytope, derived from odd CAT inequalities and lifted cycle inequalities for the asymmetric polytope.