Smaller Extended Formulations for the Spanning Tree Polytope of   Bounded-genus Graphs
  We give an $O(g^{1/2} n^{3/2} + g^{3/2} n^{1/2})$-size extended formulation for the spanning tree polytope of an $n$-vertex graph embedded on a surface of genus $g$, improving on the known $O(n^2 + g n)$-size extended formulations following from Wong and Martin. 
Samuel Fiorini, Tony Huynh, Gwena\"el Joret, and Kanstantsin   Pashkovich
math.CO cs.DM