{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01535",
  "author_total": 3,
  "authors": [
    {
      "name": "Kaizhe Chen"
    },
    {
      "name": "Shiping Liu"
    },
    {
      "name": "Haotian Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bhhngb43548e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01535",
  "fulltext_url": null,
  "id": "2bhhngb43548e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01535",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bhhngb43548e.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A rigidity theorem for edge-connectivity under non-negative Bakry--Émery curvature",
  "title_text": "A rigidity theorem for edge-connectivity under non-negative Bakry--Émery curvature",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/2bhhngb43548e",
  "venue": "arXiv",
  "versions": []
}