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arXiv · 2603.17997

The Ferrers bound for spanning trees in bipartite graphs

Boon Suan Ho
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Abstract

We prove Ehrenborg's conjecture that every connected bipartite graph $G$ with parts of size $m$ and $n$ has at most $\frac{1}{mn}\prod_{v\in V(G)} \operatorname{deg}(v)$ spanning trees, and that equality holds if and only if $G$ is a Ferrers graph. The proof is fully formalized in Lean 4.

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Boon Suan Ho. 2026-03-18. The Ferrers bound for spanning trees in bipartite graphs. https://arxiv.org/abs/2603.17997

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