A Winner Classification for Rooted Partizan Edge Geography on Heterogeneous Bouquets of Cycles
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Tilèpe, Adam
Institution: La Rochelle Université
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223690749