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Extended Formulations for Independence Polytopes of Regular Matroids

A Correction to this article was published on 16 December 2019

This article has been updated


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.

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  • 16 December 2019

    We report a logical error in our article that turns out to be fatal for the main result. The error lies in Lemma 3 for the case of a 3-sum, that is

  • 16 December 2019

    We report a logical error in our article that turns out to be fatal for the main result. The error lies in Lemma 3 for the case of a 3-sum, that is


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

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Correspondence to Stefan Weltge.

Additional information

V. Kaibel and S. Weltge acknowledge support by Deutsche Forschungsgemeinschaft (KA 1616/4-1). J. Lee was partially supported by NSF grant CMMI–1160915 and ONR grant N00014-14-1-0315.

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Kaibel, V., Lee, J., Walter, M. et al. Extended Formulations for Independence Polytopes of Regular Matroids. Graphs and Combinatorics 32, 1931–1944 (2016).

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  • Extended formulation
  • Independence polytope
  • Regular matroid
  • Decomposition

Mathematics Subject Classification

  • 52Bxx