Edge-connectivity and non-negative Lin-Lu-Yau curvature
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914463686328320 |
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| author | Liu, Shiping Xia, Qing |
| author_facet | Liu, Shiping Xia, Qing |
| contents | By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with non-negative Lin-Lu-Yau curvature is equal to its minimum degree. This answers an open question of Chen, Liu and You. Notice that our conclusion would be false if we did not require the graph to be finite. We actually classify all connected graphs with non-negative Lin-Lu-Yau curvature and edge-connectivity smaller than their minimum degree. In particular, they are all infinite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edge-connectivity and non-negative Lin-Lu-Yau curvature Liu, Shiping Xia, Qing Combinatorics Differential Geometry By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with non-negative Lin-Lu-Yau curvature is equal to its minimum degree. This answers an open question of Chen, Liu and You. Notice that our conclusion would be false if we did not require the graph to be finite. We actually classify all connected graphs with non-negative Lin-Lu-Yau curvature and edge-connectivity smaller than their minimum degree. In particular, they are all infinite. |
| title | Edge-connectivity and non-negative Lin-Lu-Yau curvature |
| topic | Combinatorics Differential Geometry |
| url | https://arxiv.org/abs/2508.20950 |