发表机构
University of Central Florida（中佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在最小度至少为 $t-1$ 且每条边具有正 Lin--Lu--Yau Ricci 曲率的无 $K_t$ 子式连通图中，最大度为 $O(t^5\log^{3/2}t)$，阶为 $O(t^{31}\log^9 t)$，并推广到局部有限图。
AI 中文摘要
受最近在禁止子式或禁止子图条件及最小度假设下具有正 Lin--Lu--Yau Ricci 曲率的连通图的阶的结果的启发，我们证明：对于每个整数 $t\ge 5$，每个没有 $K_t$ 子式、最小度至少为 $t-1$ 且每条边上具有正 Lin--Lu--Yau Ricci 曲率的连通图 $G$ 满足 \\[ \Delta(G)=O(t^5\log^{3/2}t) \quad\text{且}\quad |V(G)|<2t\Delta(G)^6=O(t^{31}\log^9 t). \\] 最小度条件 $t-1$ 是最优的。此外，最大度 $\Delta(G)$ 的界可推广到局部有限图，因此，满足这些条件的每个连通局部有限图都是有限的。
英文摘要
Motivated by recent results on the order of connected graphs with positive Lin--Lu--Yau Ricci curvature under forbidden minor or forbidden subgraph conditions and minimum degree assumptions, we prove that, for every integer $t\ge 5$, every connected graph $G$ with no $K_t$ minor, minimum degree at least $t-1$ and positive Lin--Lu--Yau Ricci curvature on every edge satisfies \[ Δ(G)=O(t^5\log^{3/2}t) \quad\text{and}\quad |V(G)|<2tΔ(G)^6=O(t^{31}\log^9 t). \] The minimum degree condition $t-1$ is best possible. Moreover, the bound on the maximum degree $Δ(G)$ extends to locally finite graphs and, consequently, every connected locally finite graph satisfying these conditions is finite.
