Four lifting theorems are derived for the symmetric travelling salesman polytope. They provide constructions and state conditions under which a linear inequality which defines a facet of the n-city travelling salesman polytope retains its facetial property for the (n + m)-city travelling salesman polytope, where m ≥ 1 is an arbitrary integer. In particular, they permit a proof that all subtour-elimination as well as comb inequalities define facets of the convex hull of tours of the n-city travelling salesman problem, where n is an arbitrary integer. © 1979 The Mathematical Programming Society.
