Recently, Andersen et al. [1] and Borozan and Cornuéjols [3] characterized the minimal inequalities of a system of two rows with two free integer variables and nonnegative continuous variables. These inequalities are either split cuts or intersection cuts derived using maximal lattice-free convex sets. In order to use these minimal inequalities to obtain cuts from two rows of a general simplex ...

We prove that any mixed-integer linear extended formulation for the matching polytope of the complete graph on n vertices, with a polynomial number of constraints, requires Ω( √ n/logn) many integer variables. By known reductions, this result extends to the traveling salesman polytope. This lower bound has various implications regarding the existence of small mixed-integer mathematical formulat...