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PreprintarXiv licencearXiv

A rigidity theorem for edge-connectivity under non-negative Bakry--Émery curvature

  • Kaizhe Chen
  • Shiping Liu
  • Haotian Yang
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Abstract

The edge-connectivity κ(G) of a graph G is the minimum number of edges whose removal disconnects G, and it is bounded above by the minimum degree δ(G). We classify all connected locally finite simple graphs with nonnegative Bakry--Émery curvature satisfying κ(G)<δ(G). All such graphs are infinite. Consequently, every finite connected simple graph with nonnegative Bakry--Émery curvature satisfies κ(G)=δ(G), confirming a conjecture of Chen, Koolen, and Liu.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026rigidity,
  title = {{A rigidity theorem for edge-connectivity under non-negative Bakry--Émery curvature}},
  author = {Kaizhe Chen and Shiping Liu and Haotian Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01535},
  eprint = {2611.01535},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01535},
}
RIS
TY  - UNPB
TI  - A rigidity theorem for edge-connectivity under non-negative Bakry--Émery curvature
AU  - Kaizhe Chen
AU  - Shiping Liu
AU  - Haotian Yang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01535
UR  - https://arxiv.org/abs/2611.01535
AB  - The edge-connectivity κ(G) of a graph G is the minimum number of edges whose removal disconnects G, and it is bounded above by the minimum degree δ(G). We classify all connected locally finite simple graphs with nonnegative Bakry--Émery curvature satisfying κ(G)<δ(G). All such graphs are infinite. Consequently, every finite connected simple graph with nonnegative Bakry--Émery curvature satisfies κ(G)=δ(G), confirming a conjecture of Chen, Koolen, and Liu.
ER  -