{
  "abstract": "For integers $1\\le k\\le n/2$, let $f(k,n)$ be the least integer $s$ such that every $s$-connected graph on $n$ vertices contains a spanning bipartite $k$-connected subgraph. Thomassen conjectured that $f(k,n)$ is bounded by a function of $k$ alone. Delcourt and Ferber proved $f(k,n)=O(k^3\\log n)$, and Yuster subsequently obtained $f(k,n)\\le22k^2\\log_2 n$. We prove that, for $2\\le k\\le n/2$, \\[ f(k,n)\\le\\min\\left\\{n-1,\\, \\left\\lfloor6(k-1)\\log_2\\frac{n}{k-1}\\right\\rfloor\\right\\}. \\] In particular, $f(k,n)=O(k\\log(n/k))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23262",
  "author_total": 3,
  "authors": [
    {
      "name": "G. Gutin"
    },
    {
      "name": "Y. Hao"
    },
    {
      "name": "Y. Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/860768k6xp5tc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23262",
  "fulltext_url": null,
  "id": "860768k6xp5tc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23262",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214036203",
  "pdf_url": "https://arxiv.org/pdf/2609.23262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/860768k6xp5tc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23262"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An $O(k\\log(n/k))$ Bound on Spanning Bipartite Connectivity",
  "title_text": "An O(klog(n/k)) Bound on Spanning Bipartite Connectivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/860768k6xp5tc",
  "venue": "arXiv",
  "versions": []
}