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.

Comments

First published in Involve: A Journal of Mathematics, Vol. 18, 2025, No. 1, published by Mathematical Sciences Publishers.

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

Included in

Mathematics Commons

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