{
  "abstract": "We prove the conjecture of Borowiecki and Broere that every finite simple planar graph admits a generalized total coloring with four colors: a proper vertex coloring with four colors together with an edge coloring with four colors in which each edge color class is a forest and no edge receives the color of either endpoint. In fact every proper four-coloring of such a graph extends to an edge coloring of the required kind. The proof combines a component-count inequality for planar graphs whose vertices are partitioned into four independent sets, obtained by completing to a triangulation, with the matroid partition theorem applied to four graphic matroids. A Lean 4 formalization relative to six named background assumptions is described below.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00091",
  "author_total": 1,
  "authors": [
    {
      "name": "James Alexander Schreib"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ck34bemjd32v4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00091",
  "fulltext_url": null,
  "id": "ck34bemjd32v4",
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  "landing_url": "https://arxiv.org/abs/2610.00091",
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7216146432",
  "pdf_url": "https://arxiv.org/pdf/2610.00091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ck34bemjd32v4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Borowiecki-Broere Generalized Total Coloring Conjecture for Planar Graphs",
  "title_text": "The Borowiecki-Broere Generalized Total Coloring Conjecture for Planar Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/ck34bemjd32v4",
  "venue": "arXiv",
  "versions": []
}