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A computational
solution to the game of cycles
Jocelyn Garcia, Mike Janssen and Eliza Kautz |
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Vol. 18 (2025), No. 1, 123–140
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Abstract |
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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. |
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Keywords
game of cycles, games on graphs, game theory
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Mathematical Subject Classification
Primary: 91A46
Secondary: 91-04
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Milestones
Received: 30 May 2023
Revised: 7 September 2023
Accepted: 7 September 2023
Published: 24 January 2025
Communicated by Arthur T. Benjamin
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Authors |
| Jocelyn Garcia | |
| Department of Computer Science Tufts University Medford, MA United States |
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| Mike Janssen | |
| Mathematics and Statistics Dordt University Sioux Center, IA United States |
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| Eliza Kautz | |
| Mathematics and Statistics Dordt University Sioux Center, IA United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
