{
  "abstract": "For a graph $G$, let $τ_{\\mathrm{iso}}(G)$ denote the number of isomorphism classes of its spanning trees. For every fixed $d\\ge3$ and all sufficiently large $n$, we prove that every connected $n$-vertex graph $G$ with $δ(G)\\ge d$ satisfies \\[τ_{\\mathrm{iso}}(G)\\ge τ_{\\mathrm{iso}}(K_{d,n-d})=A_dn^{d-1}+O_d(n^{d-2}),\\] for an explicit constant $A_d>0$, and $K_{d,n-d}$ is the unique minimizer. This confirms a conjecture of Bitonti, Michel and Scott and extends it to every $d\\ge3$. We also show that any such graph with $O(n^{d-1})$ spanning-tree types has all but a bounded number of vertices with the same $d$ neighbours.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30201",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhifei Yan"
    },
    {
      "name": "Lu-Ming Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mdnfrg25dw3k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30201",
  "fulltext_url": null,
  "id": "1mdnfrg25dw3k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30201",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214372595",
  "pdf_url": "https://arxiv.org/pdf/2609.30201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mdnfrg25dw3k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An extremal theorem for non-isomorphic spanning trees",
  "title_text": "An extremal theorem for non-isomorphic spanning trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/1mdnfrg25dw3k",
  "venue": "arXiv",
  "versions": []
}