{
  "abstract": "Motivated by recent results on the order of connected graphs with positive Lin--Lu--Yau Ricci curvature under forbidden minor or forbidden subgraph conditions and minimum degree assumptions, we prove that, for every integer $t\\ge 5$, every locally finite graph $G$ with no $K_t$ minor, minimum degree at least $t-1$ and positive Lin--Lu--Yau Ricci curvature on every edge satisfies \\[ Δ(G)=O(t^5\\log^{3/2}t). \\] The minimum degree condition $t-1$ is best possible. Moreover, if $G$ is connected, then $G$ is finite and \\[|V(G)|<2tΔ(G)^6=O(t^{31}\\log^9 t). \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08706",
  "author_total": 1,
  "authors": [
    {
      "name": "Zi-Xia Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45qhhgewjtsdv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08706",
  "fulltext_url": null,
  "id": "45qhhgewjtsdv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08706",
  "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": "W7221055382",
  "pdf_url": "https://arxiv.org/pdf/2610.08706",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45qhhgewjtsdv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.08706",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08706"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the maximum degree and order of $K_t$-minor-free graphs with positive Lin--Lu--Yau curvature",
  "title_text": "On the maximum degree and order of K_t-minor-free graphs with positive Lin--Lu--Yau curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/45qhhgewjtsdv",
  "venue": "arXiv",
  "versions": []
}