{
  "abstract": "Kühn and Osthus proved that, for every positive integer $\\ell$, every $2^{16}\\ell^2$-connected graph $G$ has a partition $V(G)=S\\cup T$ such that $G[S]$ and $G[T]$ are $\\ell$-connected and $d_T(v)\\geq \\ell$ for every $v\\in S$. And they asked whether the quadratic bound can be replaced by a linear bound. In this paper, we answer this question in the affirmative by proving that every $641\\ell$-connected graph $G$ has a partition $V(G)=S\\cup T$ such that $G[S]$ and $G[T]$ are $\\ell$-connected and $d_T(v)\\ge \\ell$ for every $v\\in S$. The proof integrates the Moser-Tardos resampling algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09365",
  "author_total": 3,
  "authors": [
    {
      "name": "Jia Zhou"
    },
    {
      "name": "Jin Yan"
    },
    {
      "name": "Yunshu Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bce2m45w5j3m3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09365",
  "fulltext_url": null,
  "id": "bce2m45w5j3m3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09365",
  "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": "W7220937252",
  "pdf_url": "https://arxiv.org/pdf/2610.09365",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bce2m45w5j3m3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09365",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09365"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A linear bound for a connectivity partition in graphs",
  "title_text": "A linear bound for a connectivity partition in graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/bce2m45w5j3m3",
  "venue": "arXiv",
  "versions": []
}