Research demonstrates edge-connectivity estimates and perfect matching existence in regular graphs, indicating significant geometric properties.
We establish a sharp edge‐connectivity estimate for graphs with non‐negative Bakry–Émery 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–Émery 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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Chen et al. (2026) studied this question.
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