Theory of linear and integer programming
Theory of linear and integer programming
Small travelling salesman polytopes
Mathematics of Operations Research
Mathematical Programming: Series A and B
The traveling salesman problem in graphs with some excluded minors
Mathematical Programming: Series A and B
The graphical relaxation: a new framework for the Symmetric Traveling Salesman Polytope
Mathematical Programming: Series A and B
Worst-case comparison of valid inequalities for the TSP
Mathematical Programming: Series A and B
Separating over Classes of TSP Inequalities Defined by 0 Node-Lifting in Polynominal Time
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
TSP Cuts Which Do Not Conform to the Template Paradigm
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Separation Algorithms for Classes of STSP Inequalities Arising from a New STSP Relaxation
Mathematics of Operations Research
The Symmetric Traveling Salesman Polytope: New Facets from the Graphical Relaxation
Mathematics of Operations Research
Operations Research Letters
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The graphical traveling salesman problem (GTSP) has been studied as a variant of the classical symmetric traveling salesman problem (STSP) suited particularly for sparse graphs. In addition, it can be viewed as a relaxation of the STSP and employed for solving the latter to optimality as originally proposed by Naddef and Rinaldi. There is a close natural connection between the two associated polyhedra. Until now, it was not known whether there are facets in TT-form of the GTSP polyhedron which are not facets of the STSP polytope as well. In this paper we give an affirmative answer to this question for n ≥ 9 and provide a general method for constructing such facets.