Determining the Winner in a Graph Theory Game
Arts and Sciences
We are investigating who has the winning strategy in a game in which two players take turns drawing arrows trying to complete cycle cells. The game boards are graphs, objects with dots and lines between them. A cycle cell looks like a polygon (triangle, square, pentagon, etc.). We examined game boards where the winning strategy was previously unknown. Starting with a pentagon and a heptagon glued by two sides, we worked to solve multiple classes of graphs involving stacked polygons. We also explored variations of the game where cycles, as defined in graph theory, are used in place of cycle cells, which opens the game up to non-planar graphs, such as complete graphs and gives the game a graph theory twist on top of topology. The original game was described by Francis Su in his book Mathematics for Human Flourishing.
Burkholder, Eric; Fragoso, Gabe; and Barua, Christopher, "Determining the Winner in a Graph Theory Game" (2021). Symposium on Undergraduate Research and Creative Expression (SOURCE). 977.