Theory of linear and integer programming
Theory of linear and integer programming
Clique tree inequalities and the symmetric travelling salesman problem
Mathematics of Operations Research
Hermite normal form computation using modulo determinant arithmetic
Mathematics of Operations Research
Integer and combinatorial optimization
Integer and combinatorial optimization
Facets of the three-index assignment polytope
Discrete Applied Mathematics
Small travelling salesman polytopes
Mathematics of Operations Research
Optimizing over the subtour polytope of the travelling salesman problem
Mathematical Programming: Series A and B
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Clique tree inequalities define facets of the asymmetric traveling salesman polytope
Discrete Applied Mathematics
Symmetric inequalities and their composition for asymmetric travelling salesman polytopes
Mathematics of Operations Research
Mathematical Programming: Series A and B
On the Chvátal rank of polytopes in the 0/1 cube
Discrete Applied Mathematics
Cutting planes and the complexity of the integer hull
Cutting planes and the complexity of the integer hull
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Strengthening Chvátal-Gomory cuts and Gomory fractional cuts
Operations Research Letters
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The Chvátal rank of an inequality ax ≤ b with integral components and valid for the integral hull of a polyhedron P, is the minimum number of rounds of Gomory-Chvátal cutting planes needed to obtain the given inequality. The Chvátal rank is at most one if b is the integral part of the optimum value z(a) of the linear program max{ax : x ∈ P}. We show that, contrary to what was stated or implied by other authors, the converse to the latter statement, namely, the Chvátal rank is at least two if b is less than the integral part of z(a), is not true in general. We establish simple conditions for which this implication is valid, and apply these conditions to several classes of facet-inducing inequalities for travelling salesman polytopes.