边连通性与非负 Lin-Lu-Yau 曲率
组合数学
2026-04-13 v2 微分几何
摘要
按定义，连通图的边连通性不会超过其最小度数。本文证明了具有非负 Lin-Lu-Yau 曲率的有限连通图的边连通性等于其最小度数。这解决了 Chen、Liu 和 You 的一个开放问题。值得注意的是，如果不要求图为有限，则我们的结论会失效。我们实际上对所有具有非负 Lin-Lu-Yau 曲率且边连通性小于其最小度数的连通图进行了分类。特别地，这些图都是无限图。
关键词
引用
@article{arxiv.2508.20950,
title = {Edge-connectivity and non-negative Lin-Lu-Yau curvature},
author = {Shiping Liu and Qing Xia},
journal= {arXiv preprint arXiv:2508.20950},
year = {2026}
}
备注
We have not altered the main results of the article; rather, we have primarily simplified some of the proofs and carried out a systematic revision of the overall structure. Meanwhile, we have supplemented the appendix with content such as curvature verification for the involved graphs, while reducing the original article to 24 pages