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}
}