Edge-connectivity and non-negative Lin-Lu-Yau curvature
Abstract
By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with non-negative Lin-Lu-Yau curvature is equal to its minimum degree. This answers an open question of Chen, Liu and You. Notice that our conclusion would be false if we did not require the graph to be finite. We actually classify all connected graphs with non-negative Lin-Lu-Yau curvature and edge-connectivity smaller than their minimum degree. In particular, they are all infinite.
Cite
@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}
}
Comments
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