{
  "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 $\\frac{3}{2}$. 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10559",
  "author_total": 2,
  "authors": [
    {
      "name": "Ziming Zhou"
    },
    {
      "name": "Shenggui Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2q9ve7z1742tv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10559",
  "fulltext_url": null,
  "id": "2q9ve7z1742tv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10559",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221187802",
  "pdf_url": "https://arxiv.org/pdf/2610.10559",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2q9ve7z1742tv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10559",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10559"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Edge-Connectivity versus Lin--Lu--Yau Curvature",
  "title_text": "Edge-Connectivity versus Lin--Lu--Yau Curvature",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/2q9ve7z1742tv",
  "venue": "arXiv",
  "versions": []
}