Smaller Extended Formulations for the Spanning Tree Polytope of Bounded-genus Graphs

We give an $O(g^{1\mathrm{/}2}{n}^{3\mathrm{/}2}+g^{3\mathrm{/}2}{n}^{1\mathrm{/}2})$-size extended formulation for the spanning tree polytope of an $n$-vertex graph embedded on a surface of genus $g$, improving on the known $O(n^2+gn)$-size extended formulations following from Wong and Martin.