  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.
