{
  "abstract": "The notion of induced packing treewidth aims to unify classes defined by forbidden induced subgraphs or induced minors with classes defined by the existence of certain structured tree decompositions. For a graph $H$, \\emph{induced $H$-packing treewidth}, denoted by $\\treepi_{H}$, is a tree-decomposition-based graph parameter that, for each bag, measures the maximum number of pairwise anticomplete induced copies of $H$ intersecting that bag. This notion generalizes some previously studied parameters: when $H=P_1$, it is equivalent to tree-independence number, and when $H=P_2$, it is equivalent to induced matching treewidth. We prove the following: \\begin{itemize}[itemsep=2mm,leftmargin=6mm] \\item For all $a,t\\in \\mathbb{N}$, $K_{a,a}$-free graphs of bounded induced $P_t$-packing treewidth have bounded tree-independence number. This extends the previous result of Abrishami et al. [SIAM J. Discrete Math., 2025] for $t=2$, and a result of Hajebi and Spirkl who showed that $(P_t,K_{a,a})$-free graphs have bounded tree-independence number. \\item If $H$ is any fixed path or a star, then the class of graphs of bounded induced $H$-packing treewidth is $χ$-bounded. Again, this extends the previous result of Abrishami et al. [SIAM J. Discrete Math., 2025] for $H=P_2$. \\item Finally, we study the relationship between induced packing treewidth and \\emph{sim-width}, a width parameter based on branch decompositions. We show that, although \\emph{sim-width} and induced $P_3$-packing treewidth are incomparable, graphs of bounded sim-width that exclude all \\emph{$H$-obstructions}---certain graphs that force large induced $H$-packing treewidth---have bounded induced $H$-packing treewidth. This simultaneously generalizes and resolves questions posed by Abrishami et al. [SIAM J. Discrete Math., 2025] and Brettell et al. [European J. Comb., 2025]. \\end{itemize}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21615",
  "author_total": 2,
  "authors": [
    {
      "name": "Amir Nikabadi"
    },
    {
      "name": "Paweł Rzążewski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq89f8kw5c6ev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21615",
  "fulltext_url": null,
  "id": "eq89f8kw5c6ev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21615",
  "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": "W7213950280",
  "pdf_url": "https://arxiv.org/pdf/2609.21615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq89f8kw5c6ev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Induced packing treewidth II. Excluding a clique or a biclique",
  "title_text": "Induced packing treewidth II. Excluding a clique or a biclique",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/eq89f8kw5c6ev",
  "venue": "arXiv",
  "versions": []
}