São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization The Perfect Matching Polytope, Solid Bricks and the Perfect Matching Lattice

e∈F x(e). M denotes the set of all perfect matchings of G. χ denotes the incidence vector of M . Cuts: A cut of G is a subset of E that is the coboundary ∂(S) of some subset S of V . For a cut C := ∂(S), S and S are the shores of C. A cut is trivial if one of its shores is a singleton. A cut is odd if both its shores have odd cardinality. Note: This is the notation used in Bondy and Murty’s book “Graph Theory (2008)” [1]. Most optimizers use δ(S), and we ourselves used ∇(S) instead of ∂(S) in some of our papers [3]-[9].