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A computational solution to the game of cycles

Jocelyn Garcia, Mike Janssen and Eliza Kautz

Vol. 18 (2025), No. 1, 123–140
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.

Keywords
game of cycles, games on graphs, game theory
Mathematical Subject Classification
Primary: 91A46
Secondary: 91-04
Milestones
Received: 30 May 2023
Revised: 7 September 2023
Accepted: 7 September 2023
Published: 24 January 2025

Communicated by Arthur T. Benjamin
Authors
Jocelyn Garcia
Department of Computer Science
Tufts University
Medford, MA
United States
Mike Janssen
Mathematics and Statistics
Dordt University
Sioux Center, IA
United States
Eliza Kautz
Mathematics and Statistics
Dordt University
Sioux Center, IA
United States