Counting two-forests and random cut size via potential theory
Combinatorics
2023-08-09 v1 Differential Geometry
Probability
Abstract
We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity relating the number of spanning trees and two-forests to pairwise effective resistances in a graph. Along the way, we make connections to potential theoretic invariants on metric graphs.
Keywords
Cite
@article{arxiv.2308.03859,
title = {Counting two-forests and random cut size via potential theory},
author = {Harry Richman and Farbod Shokrieh and Chenxi Wu},
journal= {arXiv preprint arXiv:2308.03859},
year = {2023}
}
Comments
20 pages, 5 figures. Comments welcome!