{
  "abstract": "Monadically dependent graph classes are those in which first-order logic cannot encode all graphs. They include all nowhere dense classes and all classes of bounded twin-width. We show that first-order model checking is fixed-parameter tractable on every monadically dependent graph class. Together with the known hardness result for hereditary classes that are not monadically dependent, this gives a complete characterization of the hereditary graph classes with fixed-parameter tractable first-order model checking. This resolves a central open problem in algorithmic model theory. Our proof combines ideas from structural graph theory (graph decompositions), finite model theory (locality of first-order logic), and model theory (counting types). In particular, we show that in monadically dependent classes, tuples of fixed length have only $|U|^{O(1)}$ types of fixed quantifier rank over any set of parameters $U$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08143",
  "author_total": 3,
  "authors": [
    {
      "name": "Jan Dreier"
    },
    {
      "name": "Nikolas Mählmann"
    },
    {
      "name": "Szymon Toruńczyk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7w2f6ws9rwjpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08143",
  "fulltext_url": null,
  "id": "7w2f6ws9rwjpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08143",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08143",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7w2f6ws9rwjpc.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08143",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08143"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "First-Order Model Checking on Monadically Dependent Graph Classes",
  "title_text": "First-Order Model Checking on Monadically Dependent Graph Classes",
  "type": "preprint",
  "updated_at": "2026-11-08T18:20:59Z",
  "url": "https://research.draconitic.com/paper/7w2f6ws9rwjpc",
  "venue": "arXiv",
  "versions": []
}