{
  "abstract": "We consider an undirected edge-traversal game on a finite bouquet of simple cycles. Each of two players controls a token, both tokens begin at the common root, and the players alternate traversing edges that have not been used by either token. A player with no legal move loses. We prove that the first player wins precisely when the number of cycles of odd edge-length is odd, without assuming equal cycle lengths. The proof uses a simultaneous induction on root and defense configurations, with an exact analysis of the forced race between two opened cycles. We also explain how the classification corresponds to a completed Lean 4 formalization of the underlying game on finite edge sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40683",
  "author_total": 1,
  "authors": [
    {
      "name": "Adam Tilèpe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2ya81b5d5d83.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40683",
  "fulltext_url": null,
  "id": "f2ya81b5d5d83",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40683",
  "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",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40683",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2ya81b5d5d83.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40683",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40683"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Winner Classification for Rooted Partizan Edge Geography on Heterogeneous Bouquets of Cycles",
  "title_text": "A Winner Classification for Rooted Partizan Edge Geography on Heterogeneous Bouquets of Cycles",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/f2ya81b5d5d83",
  "venue": "arXiv",
  "versions": []
}