Determining the Winner in a Graph Theory Game
Faculty Sponsor
Zsuzsanna Szaniszlo
College
Arts and Sciences
Discipline(s)
Mathematics
Presentation Type
Oral Presentation
Symposium Date
Spring 4-29-2021
Abstract
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.
Recommended Citation
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.
https://scholar.valpo.edu/cus/977
Presentation Slides
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.