{
  "abstract": "Motivated by an analogue of pancyclicity, we study minimum-degree conditions ensuring that a $2$-connected graph $G$ of order $n$ contains a $2$-connected subgraph of every order $\\ell\\in\\{4,5,\\ldots,n\\}$. Yin and Wu [A minimum degree condition for a 2-connected graph containing all possible orders of 2-connected subgraphs, Discrete Appl. Math. 387 (2026), 129-136] initiated the study of this problem and showed that the condition $δ(G)\\ge \\lceil n/3\\rceil+1$ is sufficient. Kashima conjectured that the condition $δ(G)\\ge \\sqrt{3n}$ is sufficient. In this paper, we prove that every $2$-connected graph $G$ of order $n$ with $δ(G)\\ge 2n^{2/3}+6n^{1/3}+2$ contains a $2$-connected subgraph of every order from $4$ to $n$. In particular, this gives the first sufficient minimum-degree condition of sublinear order in $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17478",
  "author_total": 2,
  "authors": [
    {
      "name": "Kenta Ozeki"
    },
    {
      "name": "Takahiro Ueoro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vasmk0a94bek.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17478",
  "fulltext_url": null,
  "id": "1vasmk0a94bek",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17478",
  "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": "W7203794126",
  "pdf_url": "https://arxiv.org/pdf/2608.17478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vasmk0a94bek.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.17478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Sublinear Minimum-Degree Condition for $2$-Connected Subgraphs of All Orders",
  "title_text": "A Sublinear Minimum-Degree Condition for $2$-Connected Subgraphs of All Orders",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1vasmk0a94bek",
  "venue": "arXiv",
  "versions": []
}