非负Bakry--Émery曲率图的一个极值定理
An extremal theorem for graphs with non-negative Bakry--Émery curvature
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中文总结 AI 辅助
本文针对带非标准化拉普拉斯算子的非负Bakry--Émery曲率图，证明了阶数n≥7且边数超过指定阈值的图均满足CD(0,∞)，且该阈值为最优的精确极值定理。
中文摘要 AI 辅助
近期，Chen、Liu和You（论文《图的正曲率的一个极值定理》，arXiv:2607.02297）证明了正Lin--Lu--Yau曲率的极值定理，并提出了其他离散曲率的类似问题。本文针对带非标准化拉普拉斯算子的非负Bakry--Émery曲率，证明了一个精确极值定理：阶数n≥7、边数超过组合数C(n,2)-⌊n/2⌋-2的图均满足CD(0,∞)，且该阈值是最优的。
英文摘要
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.
