Determining the Winner in a Graph Theory Game

Faculty Sponsor

Zsuzsanna Szaniszlo


Arts and Sciences



Presentation Type

Oral Presentation

Symposium Date

Spring 4-29-2021


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.

Biographical Information about Author(s)

Eric Burkholder (Class of 2022) is a Mathematics and Data Science double major with a minor in Computer Science. He is the President Mathematics Club, a member of the Chess Club, and a projectionist for chapel services.

Gabe Fragoso (Class of 2022) is a Computer Science and Mathematics double major with a minor in Japanese. He is the Vice President of Japanese Club, a member of the Society of Hispanic Professional Engineers, and a member of the Asian American Pacific Islander Coalition.

Christopher Barua (Class of 2022) is a Mathematics major with a minor in General Engineering. He is the Vice President of VU Haunt and a member of the Magic: The Gathering Arena Esports Team.

Presentation_Game_of_Cycles.pdf (345 kB)
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