Regular matroids have polynomial extension complexity

09/18/2019 βˆ™ by Manuel Aprile, et al. βˆ™ 0 βˆ™

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.

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