English

Spanning Tree Bounds for Grid Graphs

Combinatorics 2022-06-06 v3 Probability

Abstract

Among subgraphs with a fixed number of vertices of the regular square lattice, we prove inequalities that essentially say that those with smaller boundaries have larger numbers of spanning trees and vice-versa. As an application, we relate two commonly used measurements of the compactness of district maps.

Keywords

Cite

@article{arxiv.2109.05987,
  title  = {Spanning Tree Bounds for Grid Graphs},
  author = {Kristopher Tapp},
  journal= {arXiv preprint arXiv:2109.05987},
  year   = {2022}
}
R2 v1 2026-06-24T05:55:07.944Z