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arXiv · 2609.08903

On the classification of regular graphs with positive Lin-Lu-Yau curvature

George Brooks·Nathanael Johnson·William Linz·Xiaonan Liu·Linyuan Lu·Wynton Vaughn
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Abstract

We prove several new structural and classification results about $d$-regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved $d$-regular graph has diameter at most $2d-2$, which improves the previously best known diameter bound obtained from the Bonnet-Myers-type theorem for positively curved graphs. We further show that every positively curved $d$-regular graph with $d\ge 3$ is $3$-connected. We classify all positively curved $3$-regular graphs, as well as all positively curved regular planar graphs.

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George Brooks, Nathanael Johnson, William Linz, Xiaonan Liu, Linyuan Lu, Wynton Vaughn. 2026-09-08. On the classification of regular graphs with positive Lin-Lu-Yau curvature. https://arxiv.org/abs/2609.08903

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