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PreprintCC0arXiv

Edge-Connectivity versus Lin--Lu--Yau Curvature

  • Ziming Zhou
  • Shenggui Zhang
Open at sourcePDFDOICite

Abstract

We systematically explore the relationship between edge-connectivity and Lin--Lu--Yau curvature for graphs. The intuition is that a connected graph with large Lin--Lu--Yau curvature should also have large edge-connectivity, and vice versa under suitable conditions. We prove that the edge-connectivity of a connected graph is bounded lower by the product of its minimum degree, its Lin--Lu--Yau curvature and the constant 3/2. We also provide two lower bounds on the edge-connectivity of a graph that guarantee positive Lin--Lu--Yau curvature, and discuss the sharpness of these bounds.

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Cite

BibTeXRIS
BibTeX
@misc{zhou2026edgeconnectivity,
  title = {{Edge-Connectivity versus Lin--Lu--Yau Curvature}},
  author = {Ziming Zhou and Shenggui Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10559},
  eprint = {2610.10559},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10559},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Edge-Connectivity versus Lin--Lu--Yau Curvature
AU  - Ziming Zhou
AU  - Shenggui Zhang
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.10559
UR  - https://arxiv.org/abs/2610.10559
AB  - We systematically explore the relationship between edge-connectivity and Lin--Lu--Yau curvature for graphs. The intuition is that a connected graph with large Lin--Lu--Yau curvature should also have large edge-connectivity, and vice versa under suitable conditions. We prove that the edge-connectivity of a connected graph is bounded lower by the product of its minimum degree, its Lin--Lu--Yau curvature and the constant 3/2. We also provide two lower bounds on the edge-connectivity of a graph that guarantee positive Lin--Lu--Yau curvature, and discuss the sharpness of these bounds.
ER  -