Let G=(V,E) be a matching covered graph, let P be its perfect matching polytope, and let L be the integer lattice generated by the integral points in P. In well-celebrated works of Lov\'asz (1987), and Carvalho, Lucchesi, and Murty (series of three papers, 2002), it was shown that: (a) L has a lattice basis consisting solely of incidence vectors of some perfect matchings of G, (b) 2x\in L for all integral x \in lin(P), and (c) if G has no Petersen brick then x\in L.
The original proofs are heavily reliant on the structure of perfect matchings, odd cuts, and removable edges in the graph. In this talk, we will give a short novel proof of these results by studying the facial structure of P and its relationship with the lattice L. In our approach, the Petersen graph emerges naturally as the only graph with a specific polyhedral formulation.
Tea and cookies will be served before the talk at 3:30 pm.