{
  "abstract": "We give a counterexample to Wormald's conjecture. A 16-vertex cubic graph, the disjoint union of $K_{3,3}$ with a 10-vertex bridged graph built from two subdivided copies of $K_4$, has no partition of its edges into two isomorphic spanning linear forests. The obstruction is parity: any such partition would force every monochromatic component to have even order while requiring a five-vertex side of a bridge to be partitioned into such components. Adjoining copies of $K_4$ gives counterexamples in every order $16+4t$. The counterexample is disconnected and leaves the connected case unresolved. The full family is verified in Lean without custom axioms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00086",
  "author_total": 1,
  "authors": [
    {
      "name": "James Alexander Schreib"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8e1vb8x20zt65.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00086",
  "fulltext_url": null,
  "id": "8e1vb8x20zt65",
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  "landing_url": "https://arxiv.org/abs/2610.00086",
  "language": null,
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  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7216509734",
  "pdf_url": "https://arxiv.org/pdf/2610.00086",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8e1vb8x20zt65.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00086",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00086"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Counterexample to Wormald's Conjecture",
  "title_text": "A Counterexample to Wormald's Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/8e1vb8x20zt65",
  "venue": "arXiv",
  "versions": []
}