Edge-connectivity of graphs with non-negative Bakry-Émery curvature and amply regular graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908464184295424 |
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| author | Chen, Kaizhe Koolen, Jack H. Liu, Shiping |
| author_facet | Chen, Kaizhe Koolen, Jack H. Liu, Shiping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18120 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edge-connectivity of graphs with non-negative Bakry-Émery curvature and amply regular graphs Chen, Kaizhe Koolen, Jack H. Liu, Shiping Combinatorics 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. |
| title | Edge-connectivity of graphs with non-negative Bakry-Émery curvature and amply regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.18120 |