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.Comment: v3: fixed some typo

On the optimality of the Arf invariant formula for graph polynomials

We prove optimality of the Arf invariant formula for the generating function of even subgraphs, or, equivalently, the Ising partition function, of a graph.Comment: Advances in Mathematics, 201