{
  "abstract": "Let $G$ be a connected graph with minimum degree at least two, positive Lin-Lu-Yau Ricci curvature, and no $K_{2,t}$ minor, where $t\\ge 3$ is an integer. We first establish tight upper bounds on the maximum degree of $G$ by showing that $Δ(G)\\le 2t+3$ for $t=4$, $Δ(G)\\le 2t+4$ for $t\\in\\{5,6\\}$, and $Δ(G)\\le 2t+2$ for all $t\\ge7$. We then prove that $G$ has at most $10$ vertices for $t=3$, and at most $(t+1)\\left(Δ(G)^2(Δ(G)-1)/2+1\\right)$ vertices for all $t\\ge 4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05519",
  "author_total": 3,
  "authors": [
    {
      "name": "Shuliang Bai"
    },
    {
      "name": "Xiaonan Liu"
    },
    {
      "name": "Zi-Xia Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9q0j1cs01q0d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05519",
  "fulltext_url": null,
  "id": "e9q0j1cs01q0d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05519",
  "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": "W7220704761",
  "pdf_url": "https://arxiv.org/pdf/2610.05519",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9q0j1cs01q0d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05519",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05519"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Positively Lin-Lu-Yau curved graphs with no $K_{2,t}$ minor",
  "title_text": "Positively Lin-Lu-Yau curved graphs with no K_2,t minor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/e9q0j1cs01q0d",
  "venue": "arXiv",
  "versions": []
}