Abstract 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.
Chen et al. (Mon,) studied this question.