{
  "abstract": "We prove several new structural and classification results about $d$-regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved $d$-regular graph has diameter at most $2d-2$, which improves the previously best known diameter bound obtained from the Bonnet-Myers-type theorem for positively curved graphs. We further show that every positively curved $d$-regular graph with $d\\ge 3$ is $3$-connected. We classify all positively curved $3$-regular graphs, as well as all positively curved regular planar graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08903",
  "author_total": 6,
  "authors": [
    {
      "name": "George Brooks"
    },
    {
      "name": "Nathanael Johnson"
    },
    {
      "name": "William Linz"
    },
    {
      "name": "Xiaonan Liu"
    },
    {
      "name": "Linyuan Lu"
    },
    {
      "name": "Wynton Vaughn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qby73zhvv496.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08903",
  "fulltext_url": null,
  "id": "9qby73zhvv496",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08903",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212017199",
  "pdf_url": "https://arxiv.org/pdf/2609.08903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9qby73zhvv496.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08903"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the classification of regular graphs with positive Lin-Lu-Yau curvature",
  "title_text": "On the classification of regular graphs with positive Lin-Lu-Yau curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/9qby73zhvv496",
  "venue": "arXiv",
  "versions": []
}