{
  "abstract": "We establish a strongly sublinear counterpart of a recent result of Chudnovsky, E S, and Lokshtanov (arXiv 2025) on treewidth and tree-independence number. Namely, we prove that a hereditary graph class has strongly sublinear tree-independence number if and only if, for every fixed clique bound, its graphs of bounded clique number have strongly sublinear treewidth. In fact, this is part of a broader equivalence theorem. For hereditary classes, these conditions are also equivalent to having clique-dependent polynomial expansion, to admitting balanced separators whose size is bounded by $Kω(G)^s |V(G)|^{1-β}$ for fixed $K,s,β>0$, and to admitting balanced clique-based separators of strongly sublinear size (equivalently, weight). Thus, we show that all these properties, which arose independently in the study of subexponential-time exact algorithms and polynomial-time approximation schemes, in fact describe the same hereditary graph classes. As a consequence of our equivalence theorem, we also show that every hereditary class $\\mathcal C$ with strongly sublinear tree-independence number admits a subexponential-time algorithm that, given $G\\in\\mathcal C$, computes a tree decomposition of $G$ with strongly sublinear independence number.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24684",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Munaro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abenjzqbpyhwc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24684",
  "fulltext_url": null,
  "id": "abenjzqbpyhwc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24684",
  "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.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7214020550",
  "pdf_url": "https://arxiv.org/pdf/2609.24684",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abenjzqbpyhwc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24684",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24684"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Clique-dependent strongly sublinear treewidth and strongly sublinear tree-independence number",
  "title_text": "Clique-dependent strongly sublinear treewidth and strongly sublinear tree-independence number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/abenjzqbpyhwc",
  "venue": "arXiv",
  "versions": []
}