Edge-connectivity of graphs with non-negative Bakry-\'Emery curvature and amply regular graphs
Combinatorics
2025-07-25 v1
Abstract
We establish a sharp edge-connectivity estimate for graphs with non-negative Bakry-\'Emery curvature. This leads to a geometric criterion for the existence of a perfect matching. Precisely, we show that any regular graph with non-negative Bakry-\'Emery curvature and an even or infinite number of vertices has a perfect matching. Through a synthesis of combinatorial and curvature-related techniques, we determine the edge-connectivity of (possibly infinite) amply regular graphs.
Keywords
Cite
@article{arxiv.2507.18120,
title = {Edge-connectivity of graphs with non-negative Bakry-\'Emery curvature and amply regular graphs},
author = {Kaizhe Chen and Jack H. Koolen and Shiping Liu},
journal= {arXiv preprint arXiv:2507.18120},
year = {2025}
}
Comments
18 pages