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Edge-connectivity of graphs with non-negative Bakry-Émery curvature and amply regular graphs (2507.18120v1)
Published 24 Jul 2025 in math.CO
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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