The authors introduce a projective approach for studying symmetric travelling salesman polytopes (STSPs). The symmetric travelling salesman polytope STSP(V) (resp., Hamiltonian path polytope HP(V)) is the convex hull of incidence vectors of all Hamiltonian cycles (resp., paths) on the complete undirected graph with node set V. For any node hℝV, HP(V) is a projection of STSP(Vℝ{h}). The authors show that HP(V) and STSP(Vℝ{h}) are isomorphic, and HP(V) is of full dimension minus one. By this projective approach, they obtain general clique-lifting results, all based on simple conditions, for deriving large new classes of STSP facets. These results apply to all known non-trivial STSP facets, and generalize clique-lifting results of Maurras, Grötschel and Padberg and Naddef and Rinaldi.
