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arXiv · 2507.18120

Edge-connectivity of graphs with non-negative Bakry-\'Emery curvature and amply regular graphs

Kaizhe Chen·Jack H. Koolen·Shiping Liu
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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.

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Kaizhe Chen, Jack H. Koolen, Shiping Liu. 2025-07-24. Edge-connectivity of graphs with non-negative Bakry-\'Emery curvature and amply regular graphs. https://arxiv.org/abs/2507.18120

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