{
  "abstract": "Balogh, Clemen and Lidický asked how large the minimum $\\ell_p$-norm of the internal-edge counts over balanced partitions of an $n$-vertex triangle-free graph can be. For each fixed $2<p<\\infty$ and all sufficiently large even $n$, we determine this value exactly for bisections and characterize all extremal graphs. They are precisely the complete bipartite graphs $K_{a,n-a}$ for which $a\\le n/2$ maximizes an explicit integer objective. All maximizing values of $a$ lie in an interval of length bounded in terms of $p$ alone. We also prove quantitative stability for the same range of $p$ and $n$: for sufficiently small $δ\\ge 0$, every $n$-vertex triangle-free graph with bisection value at least the asymptotic optimum minus $δn^2$ is within $O_p(δn^2+n)$ edge edits of a complete bipartite graph with the optimal limiting class ratio.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25902",
  "author_total": 1,
  "authors": [
    {
      "name": "Shufei Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5zyndthbqmhb6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25902",
  "fulltext_url": null,
  "id": "5zyndthbqmhb6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25902",
  "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": "W7223061249",
  "pdf_url": "https://arxiv.org/pdf/2610.25902",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5zyndthbqmhb6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25902",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25902"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Exact extremizers for $\\ell_p$-judicious bisections of triangle-free graphs",
  "title_text": "Exact extremizers for ℓ_p-judicious bisections of triangle-free graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/5zyndthbqmhb6",
  "venue": "arXiv",
  "versions": []
}