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arXiv · 2608.09180

An extremal theorem for graphs with non-negative Bakry--Émery curvature

Jiawei Xie·Zhe You
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Abstract

Recently, Chen, Liu, and You (An extremal theorem for positive curvature of graphs, arXiv:2607.02297) proved an extremal theorem for positive Lin--Lu--Yau curvature. They further proposed the similar problems for other discrete curvature. In this paper, we prove a sharp extremal theorem for non-negative Bakry--Émery curvature with non-normalized Laplacian: every graph of order \(n\geq 7\) with more than \[ \binom {n}{2}-\lfloor{\frac{n}{2}\rfloor}-2 \] edges satisfies $CD(0,\infty)$, and this threshold is optimal.

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Jiawei Xie, Zhe You. 2026-08-10. An extremal theorem for graphs with non-negative Bakry--Émery curvature. https://arxiv.org/abs/2608.09180

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