{
  "abstract": "We prove that the average order of connected induced subgraphs of a connected simple graph of order $n$ and minimum degree at least $3$ is strictly greater than $n/2$, which settles a conjecture of Vince~[\\emph{J. Graph Theory} 97 (2021), 82--103]. We go further and show that, for connected simple graphs of order $n$ and minimum degree exactly $k\\ge3$, $K_k\\vee(K_1\\cup K_{n-k-1})$ uniquely minimizes this average under additional conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27553",
  "author_total": 2,
  "authors": [
    {
      "name": "Jungang Chen"
    },
    {
      "name": "Hongxia Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cv23xe4nvg2jj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27553",
  "fulltext_url": null,
  "id": "cv23xe4nvg2jj",
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  "landing_url": "https://arxiv.org/abs/2610.27553",
  "language": null,
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  "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"
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    [
      "openalex",
      "2608|Graph theory and applications"
    ]
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  "openalex": "W7223107694",
  "pdf_url": "https://arxiv.org/pdf/2610.27553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cv23xe4nvg2jj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A proof of Vince's conjecture on the average order of connected induced subgraphs",
  "title_text": "A proof of Vince's conjecture on the average order of connected induced subgraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/cv23xe4nvg2jj",
  "venue": "arXiv",
  "versions": []
}