Regular Matroids Have Polynomial Extension Complexity

Abstract

We prove that the extension complexity of the independence polytope of every regular matroid on [Formula: see text] elements is [Formula: see text]. Past results of Wong and Martin on extended formulations of the spanning tree polytope of a graph imply a [Formula: see text] 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 [Formula: see text] bound.