{
  "abstract": "The tree-independence number $tree\\text{-}α(G)$, the induced matching treewidth $tree\\text{-}μ(G)$, and the sim-width $simw(G)$ are graph parameters defined in terms of tree or branch decompositions. We establish two polynomial bounds for the tree-independence number of induced $K_{t,t}$-free graphs, one in terms of sim-width and the other in terms of induced matching treewidth. Abrishami et al. (SIDMA, 2025) and Brettell et al. (EJC, 2025) asked whether bounded sim-width, together with the exclusion of an induced $K_{t,t}$, implies bounded tree-independence number. We answer this question by proving that, for integers $t\\geq 2$ and $s\\geq 1$, every induced $K_{t,t}$-free graph $G$ with $simw(G)\\leq s$ satisfies $tree\\text{-}α(G)=O_t\\left((s+1)^{2t^2-2t}\\right)$. This also proves a polynomial strengthening of a conjecture of Bešter Štorgel et al. (arXiv, 2026) concerning induced $K_{1,t}$-free graphs and improves a theorem of Alon et al. (arXiv, 2025) by reducing the exponent from $3t^2+1$ to $2t^2-2t$. Alon et al. (arXiv, 2025) asked whether, for fixed induced matching treewidth, the tree-independence number is polynomially bounded in $t$. Using a VC-dimension argument, we answer this question affirmatively by showing that, for integers $μ\\geq 1$ and $t\\geq 2$, every induced $K_{t,t}$-free graph $G$ with $tree\\text{-}μ(G)\\leqμ$ satisfies $tree\\text{-}α(G)=t^{O_μ(1)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18648",
  "author_total": 2,
  "authors": [
    {
      "name": "Mengyuan Niu"
    },
    {
      "name": "Xiumei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jxm7x94qcs06.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18648",
  "fulltext_url": null,
  "id": "5jxm7x94qcs06",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18648",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7213521663",
  "pdf_url": "https://arxiv.org/pdf/2609.18648",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jxm7x94qcs06.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18648",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18648"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sim-Width, Induced Matching Treewidth, and Tree-Independence Number in Induced $K_{t,t}$-Free Graphs",
  "title_text": "Sim-Width, Induced Matching Treewidth, and Tree-Independence Number in Induced K_t,t-Free Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/5jxm7x94qcs06",
  "venue": "arXiv",
  "versions": []
}