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arXiv · 2611.01535

A rigidity theorem for edge-connectivity under non-negative Bakry--Émery curvature

Kaizhe Chen·Shiping Liu·Haotian Yang
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Abstract

The edge-connectivity $κ(G)$ of a graph $G$ is the minimum number of edges whose removal disconnects $G$, and it is bounded above by the minimum degree $δ(G)$. We classify all connected locally finite simple graphs with nonnegative Bakry--Émery curvature satisfying $κ(G)<δ(G)$. All such graphs are infinite. Consequently, every finite connected simple graph with nonnegative Bakry--Émery curvature satisfies $κ(G)=δ(G)$, confirming a conjecture of Chen, Koolen, and Liu.

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Kaizhe Chen, Shiping Liu, Haotian Yang. 2026-11-01. A rigidity theorem for edge-connectivity under non-negative Bakry--Émery curvature. https://arxiv.org/abs/2611.01535

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