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A Winner Classification for Rooted Partizan Edge Geography on Heterogeneous Bouquets of Cycles — arXiv:2610.40683

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40683
License (as archived): CC0-1.0
Archived: 2026-11-02T05:00:25.494Z
SHA-256 of the archived text: 2cbc9b345de4c983d34a2396bcc75a8c1be106bb0c93ba513bee955461934ea2
Stable URL of this page: https://metraipolis.com/documento/dc_337448def262

How to cite

A Winner Classification for Rooted Partizan Edge Geography on Heterogeneous Bouquets of Cycles — arXiv:2610.40683 — arXiv (en), https://arxiv.org/abs/2610.40683 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_337448def262 (Metraipolis archive dc_337448def262, sha256 2cbc9b345de4c983d34a2396bcc75a8c1be106bb0c93ba513bee955461934ea2)

BibTeX

@misc{dc337448def262,
  title = {A Winner Classification for Rooted Partizan Edge Geography on Heterogeneous Bouquets of Cycles — arXiv:2610.40683},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40683},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_337448def262; sha256 2cbc9b345de4c983d34a2396bcc75a8c1be106bb0c93ba513bee955461934ea2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40683. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.40683 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-02T04:47:57.649Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).