The Game of Cycles
Ryan Alvarado, Maia Averett, Benjamin Gaines, Christopher Jackson, Mary Leah Karker, Małgorzata Marciniak, Francis Edward Su, Shanise Walker · American Mathematical Monthly · 2021
The Game of Cycles, introduced by Su in 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.