Graphs and Combinatorics

, Volume 32, Issue 5, pp 1931–1944

# Extended Formulations for Independence Polytopes of Regular Matroids

• Volker Kaibel
• Jon Lee
• Matthias Walter
• Stefan Weltge
Original Paper

## Abstract

We show that the independence polytope of every regular matroid has an extended formulation of size quadratic in the size of its ground set. This generalizes a similar statement for (co-)graphic matroids, which is a simple consequence of Martin’s extended formulation for the spanning-tree polytope. In our construction, we make use of Seymour’s decomposition theorem for regular matroids. As a consequence, the extended formulations can be computed in polynomial time.

### Keywords

Extended formulation Independence polytope Regular matroid Decomposition

52Bxx

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## Authors and Affiliations

• Volker Kaibel
• 1
• Jon Lee
• 2
• Matthias Walter
• 1
• Stefan Weltge
• 1
1. 1.Institut für Mathematische Optimierung, Otto-von-Guericke-Universität MagdeburgMagdeburgGermany
2. 2.Department of Industrial and Operations EngineeringThe University of MichiganAnn ArborUSA