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arXiv · 1909.08539

Regular matroids have polynomial extension complexity

Manuel Aprile·Samuel Fiorini
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Abstract

We prove that the extension complexity of the independence polytope of every regular matroid on $n$ elements is $O(n^6)$. Past results of Wong and Martin on extended formulations of the spanning tree polytope of a graph imply a $O(n^2)$ bound for the special case of (co)graphic matroids. However, the case of a general regular matroid was open, despite recent attempts. We also consider the extension complexity of circuit dominants of regular matroids, for which we give a $O(n^2)$ bound.

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Manuel Aprile, Samuel Fiorini. 2019-12-20. Regular matroids have polynomial extension complexity. https://arxiv.org/abs/1909.08539

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