Integer and combinatorial optimization
Integer and combinatorial optimization
A recursive procedure to generate all cuts for 0-1 mixed integer programs
Mathematical Programming: Series A and B
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Combinatorial optimization
On the matrix-cut rank of polyhedra: 19
Mathematics of Operations Research
When Does the Positive Semidefiniteness Constraint Help in Lifting Procedures?
Mathematics of Operations Research
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
Elementary closures for integer programs
Operations Research Letters
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Eisenbrand and Schulz showed recently (IPCO 99) that the maximum Chvátal rank of a polytope in the [0, 1]n cube is bounded above by O(n2logn) and bounded below by (1 + Ɛ)n for some Ɛ 0. It is well known that Chvátal's cuts are equivalent to Gomory's fractional cuts, which are themselves dominated by Gomory's mixed integer cuts. What do these upper and lower bounds become when the rank is defined relative to Gomory's mixed integer cuts? An upper bound of n follows from existing results in the literature. In this note, we show that the lower bound is also equal to n. We relate this result to bounds on the disjunctive rank and on the Lovász-Schrijver rank of polytopes in the [0, 1]n cube. The result still holds for mixed 0,1 polyhedra with n binary variables.