Graphs and Combinatorics

, Volume 32, Issue 5, pp 1931–1944 | Cite as

Extended Formulations for Independence Polytopes of Regular Matroids

  • Volker Kaibel
  • Jon Lee
  • Matthias Walter
  • Stefan WeltgeEmail author
Original Paper


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.


Extended formulation Independence polytope Regular matroid Decomposition 

Mathematics Subject Classification




We would like to thank Klaus Truemper for valuable comments on the decomposition of matroids.


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Copyright information

© Springer Japan 2016

Authors and Affiliations

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

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