Stable sets, corner polyhedra and the Chvátal closure

Authors:
Manoel CampêLo;GéRard CornuéJols
Affiliations:
Departamento de Estatística e Matemática Aplicada, Universidade Federal do Ceará, Brazil;Tepper School of Business, Carnegie Mellon University, Pitsburgh, PA 15213, United States
Venue:
Operations Research Letters
Year:
2009

Citing 9
Cited 0

Matrices with the Edmonds-Johnson property

Combinatorica
{0, 12 }-Chva´tal-Gomory cuts

Mathematical Programming: Series A and B
Split closure and intersection cuts

Mathematical Programming: Series A and B
The stable set polytope of quasi-line graphs

Combinatorica
Inequalities from Two Rows of a Simplex Tableau

IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On the facets of mixed integer programs with two integer variables and two constraints

Mathematical Programming: Series A and B
Minimal Valid Inequalities for Integer Constraints

Mathematics of Operations Research
On an Analysis of the Strength of Mixed-Integer Cutting Planes from Multiple Simplex Tableau Rows

SIAM Journal on Optimization
On the relative strength of split, triangle and quadrilateral cuts

Mathematical Programming: Series A and B

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the edge formulation of the stable set problem. We characterize its corner polyhedron, i.e. the convex hull of the points satisfying all the constraints except the non-negativity of the basic variables. We show that the non-trivial inequalities necessary to describe this polyhedron can be derived from one row of the simplex tableau as fractional Gomory cuts. It follows that the split closure is not stronger than the Chvatal closure for the edge relaxation of the stable set problem.