发表机构
Northwestern Polytechnical University; Xi’an-Budapest Joint Research Center for Combinatorics（西北工业大学; 西安-布达佩斯组合学联合研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究系统探究图的边连通度与Lin--Lu--Yau曲率的关系，证明连通图边连通度的下界由最小度、Lin--Lu--Yau曲率与$\frac{3}{2}$的乘积给出，还给出保证正Lin--Lu--Yau曲率的边连通度下界并讨论其尖锐性。
AI 中文摘要
我们系统探究图的边连通度与Lin--Lu--Yau曲率之间的关系。直观来看，具有较大Lin--Lu--Yau曲率的连通图应也具有较大的边连通度，且在合适条件下反之亦然。我们证明，连通图的边连通度下界由其最小度、Lin--Lu--Yau曲率与常数$\frac{3}{2}$的乘积给出。我们还给出图边连通度的两个下界，以保证其具有正Lin--Lu--Yau曲率，并讨论这些下界的尖锐性。
英文摘要
We systematically explore the relationship between edge-connectivity and Lin--Lu--Yau curvature for graphs. The intuition is that a connected graph with large Lin--Lu--Yau curvature should also have large edge-connectivity, and vice versa under suitable conditions. We prove that the edge-connectivity of a connected graph is bounded lower by the product of its minimum degree, its Lin--Lu--Yau curvature and the constant $\frac{3}{2}$. We also provide two lower bounds on the edge-connectivity of a graph that guarantee positive Lin--Lu--Yau curvature, and discuss the sharpness of these bounds.
