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arXiv · 2308.03859

Counting two-forests and random cut size via potential theory

Harry Richman·Farbod Shokrieh·Chenxi Wu
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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.

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Harry Richman, Farbod Shokrieh, Chenxi Wu. 2023-08-07. Counting two-forests and random cut size via potential theory. https://arxiv.org/abs/2308.03859

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