Clique tree inequalities and the symmetric travelling salesman problem
Mathematics of Operations Research
Integer and combinatorial optimization
Integer and combinatorial optimization
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
Handbook of combinatorics (vol. 2)
On the monotonization of polyhedra
Mathematical Programming: Series A and B
The Symmetric Traveling Salesman Polytope Revisited
Mathematics of Operations Research
Not every GTSP facet induces an STSP facet
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Generalized Domino-Parity Inequalities for the Symmetric Traveling Salesman Problem
Mathematics of Operations Research
Generalized Domino-Parity Inequalities for the Symmetric Traveling Salesman Problem
Mathematics of Operations Research
Certification of an optimal TSP tour through 85,900 cities
Operations Research Letters
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The path, the wheelbarrow, and the bicycle inequalities have been shown by Cornuéjols, Fonlupt, and Naddef to be facet-defining for the graphical relaxation of STSP(n), the polytope of the symmetric traveling salesman problem on an n-node complete graph. We show that these inequalities, and some generalizations of them, define facets also for STSP(n). In conclusion, we characterize a large family of facet-defining inequalities for STSP(n) that include, as special cases, most of the inequalities currently known to have this property as the comb, the clique tree, and the chain inequalities. Most of the results given here come from a strong relationship of STSP(n) with its graphical relaxation that we have pointed out in another paper, where the basic proof techniques are also described.