{
  "abstract": "The tree-independence number of a graph is the minimum, over all tree-decompositions of the graph, of the maximum size of an independent set contained in a bag. Graph classes of bounded tree-independence number have strong structural and algorithmic properties; however, the parameter can be unbounded even in quite restricted classes. In particular, the presence of an induced biclique $K_{\\ell,\\ell}$ forces tree-independence number at least $\\ell$. This leads to the question whether large induced bicliques are the only obstruction to bounded tree-independence number in natural hereditary classes. A conjecture of Dallard, Krnc, Kwon, Milanič, Munaro, Štorgel, and Wiederrecht states that for all positive integers $t$ and $\\ell$, ${\\{P_t,K_{\\ell,\\ell}\\}}$-free graphs have bounded tree-independence number. We prove this conjecture for ${t=5}$ by showing that every ${\\{P_5,K_{\\ell,\\ell}\\}}$-free graph has tree-independence number at most ${4\\ell-4}$. We also obtain related bounds for the weaker parameter of $α$-degeneracy and answer a question of Hilaire, Milanič, and Vasić whether tree-independence number of ${\\{P_5,K_{\\ell,\\ell}\\}}$-free graphs exceeds $\\ell$ by at most an additive constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.03965",
  "author_total": 8,
  "authors": [
    {
      "name": "Václav Blažej"
    },
    {
      "name": "J. Pascal Gollin"
    },
    {
      "name": "Tomáš Hons"
    },
    {
      "name": "Tomáš Masařík"
    },
    {
      "name": "Martin Milanič"
    },
    {
      "name": "Paweł Rzążewski"
    },
    {
      "name": "Ondřej Suchý"
    },
    {
      "name": "Alexandra Wesolek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwk2fj7ecdrq1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.03965",
  "fulltext_url": null,
  "id": "bwk2fj7ecdrq1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.03965",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7160428726",
  "pdf_url": "https://arxiv.org/pdf/2605.03965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwk2fj7ecdrq1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2605.03965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.03965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tree-independence number of $P_5$-free graphs with no large bicliques",
  "title_text": "Tree-independence number of P_5-free graphs with no large bicliques",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/bwk2fj7ecdrq1",
  "venue": "arXiv",
  "versions": []
}