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

TL;DR

This paper presents a significantly smaller extended formulation for the spanning tree polytope of bounded-genus graphs, improving the size bounds compared to previous methods.

Contribution

It introduces an extended formulation with size $O(g^{1/2} n^{3/2} + g^{3/2} n^{1/2})$, advancing the understanding of polytope representations for bounded-genus graphs.

Findings

Reduced the size of extended formulations for bounded-genus graphs

Improved bounds from $O(n^2 + g n)$ to $O(g^{1/2} n^{3/2} + g^{3/2} n^{1/2})$

Provides a more efficient polyhedral description of the spanning tree polytope

Abstract

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.