Document Type
Article
Publication Date
2025
Department
Mathematics, Statistics, and Computer Science
Keywords
game of cycles, games on graphs, game theory
Abstract
In Mathematics for Human Flourishing, Francis E. Su introduced The Game of Cycles, a game played on a finite simple planar graph. In game play, opponents alternate adding direction to the edges of the graph with the goal of creating a cycle or making the last legal move. Recent work has sought to determine winning strategies on certain classes of graphs. We introduce a tabular representation of a game state and provide a computer program that determines which player has a winning strategy on any legal game board. The program builds a directed graph of all possible game states, utilizing concepts of impartial game theory in the labeling of game states and determination of winning strategies.
Source Publication Title
Involve: A Journal of Mathematics
Publisher
Mathematical Sciences Publishers
Volume
18
Issue
1
First Page
123
DOI
10.2140/involve.2025.18.123
Recommended Citation
Garcia, J., Janssen, M., & Kautz, E. (2025). A Computational Approach to the Game of Cycles. Involve: A Journal of Mathematics, 18 (1), 123. https://doi.org/10.2140/involve.2025.18.123
Comments
First published in Involve: A Journal of Mathematics, Vol. 18, 2025, No. 1, published by Mathematical Sciences Publishers.