{
  "abstract": "We show that every planar graph with no $t \\times t$ grid minor has treewidth at most $4t +4$. This improves on the previously best known bound of $\\frac{9}{2}t - \\frac{11}{2}$, due to Gu and Tamaki (2012), and is within a factor $2$ of optimal. A key step in the proof is showing the following result, which might be of independent interest: Every $2$-connected plane graph $G$ with radius $d$ and faces of size at most $k$ has a tree-decomposition of width at most $\\max\\{3d+ k+5, 2d+2k+1\\}$ such that the vertex set of every face of $G$ is contained in some bag.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15596",
  "author_total": 6,
  "authors": [
    {
      "name": "Wouter Cames van Batenburg"
    },
    {
      "name": "Quentin Claus"
    },
    {
      "name": "Gwenaël Joret"
    },
    {
      "name": "Robin Petit"
    },
    {
      "name": "Jean-Florent Raymond"
    },
    {
      "name": "Eileen Robinson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xjf3y9bw6xfm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15596",
  "fulltext_url": null,
  "id": "8xjf3y9bw6xfm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15596",
  "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": "W7213345936",
  "pdf_url": "https://arxiv.org/pdf/2609.15596",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xjf3y9bw6xfm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15596",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15596"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An improved bound on the treewidth of planar graphs excluding a grid minor",
  "title_text": "An improved bound on the treewidth of planar graphs excluding a grid minor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8xjf3y9bw6xfm",
  "venue": "arXiv",
  "versions": []
}