{
  "abstract": "Let $G$ be a simple graph on $n$ vertices, and let $F(G)$ denote the number of its spanning forests. Bencs and Csikvári [Upper bound for the number of spanning forests of regular graphs, European J. Combin. 110 (2023) 103677] proved that every $r$-regular graph $G$ with $r\\geq 2$ satisfies $F(G) \\leq r^{n}$. They further conjectured that for $r \\geq 3$, \\[ F(G)^{1/n} \\leq \\frac{(r - 1)^{r-1}}{(r^2 - 2r - 1)^{r/2-1}}. \\] In this paper, we resolve this conjecture in the affirmative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05722",
  "author_total": 3,
  "authors": [
    {
      "name": "T. Wu"
    },
    {
      "name": "S. Lu"
    },
    {
      "name": "X. Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ae0h6pav4s2qs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05722",
  "fulltext_url": null,
  "id": "ae0h6pav4s2qs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05722",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7220697982",
  "pdf_url": "https://arxiv.org/pdf/2610.05722",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ae0h6pav4s2qs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05722",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05722"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A sharp upper bound on the number of spanning forests of regular graphs",
  "title_text": "A sharp upper bound on the number of spanning forests of regular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ae0h6pav4s2qs",
  "venue": "arXiv",
  "versions": []
}