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arXiv · 2004.00776

The Game of Cycles

Ryan Alvarado·Maia Averett·Benjamin Gaines·Christopher Jackson·Mary Leah Karker·Malgorzata Aneta Marciniak·Francis Su·Shanise Walker
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Abstract

The Game of Cycles, introduced by Su (2020), is played on a simple connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a topological flavor. The object of the game is to produce a cycle cell---a cell surrounded by arrows all cycling in one direction---or to make the last possible move. We analyze the two-player game for various classes of graphs and determine who has a winning strategy. We also establish a topological property of the game: that a board with every edge marked must have a cycle cell.

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Ryan Alvarado, Maia Averett, Benjamin Gaines, Christopher Jackson, Mary Leah Karker, Malgorzata Aneta Marciniak, Francis Su, Shanise Walker. 2020-04-02. The Game of Cycles. https://arxiv.org/abs/2004.00776

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