{
  "abstract": "A graph class $\\mathcal{C}$ is monadically dependent if one cannot interpret all graphs in vertex-colored graphs from $\\mathcal{C}$ using a fixed formula of first-order logic. We prove that every monadically dependent graph class has almost bounded merge-width, thereby confirming a conjecture of the first and the last author [STOC '25]. Our proof is algorithmic and the witnessing decompositions in the form of merge sequences can be computed in nearly-cubic time. This is a step towards the proof of fixed-parameter tractability of model checking first-order logic on monadically dependent graph classes, which is achieved in a companion paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06804",
  "author_total": 4,
  "authors": [
    {
      "name": "Jan Dreier"
    },
    {
      "name": "Nikolas Mählmann"
    },
    {
      "name": "Michał Pilipczuk"
    },
    {
      "name": "Szymon Toruńczyk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9z6b256x6vfw0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06804",
  "fulltext_url": null,
  "id": "9z6b256x6vfw0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06804",
  "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/2611.06804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9z6b256x6vfw0.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06804"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Monadically Dependent Graph Classes Have Almost Bounded Merge-Width",
  "title_text": "Monadically Dependent Graph Classes Have Almost Bounded Merge-Width",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/9z6b256x6vfw0",
  "venue": "arXiv",
  "versions": []
}