Some results on node lifting of TSP inequalities (Q1592839)

This paper deals with facet-defining inequalities for the symmetric traveling salesman polytope, in particular those that can be obtained by performing \textit{D. Naddef} and \textit{G. Rinaldi}'s node lifting operation [Math. Program. 58A, 53-88 (1992; Zbl 0780.90103)]. 0-node lifting and generalizations are reviewed in sections 2 and 3. The main results are in sections 3 and 4, where it is shown -- that 1-node lifting of cut-based inequalities always has a geometric interpretation if a certain claw-free condition (satisfied by most of these TSP inequalities) is met, -- that simultaneous node liftings of a subtour elimination inequality are all subtour elimination inequalities, and where a non-geometric 1-node lifting of a cut based inequality with claws, the Petersen inequality, is examined.