Conference Athletic Schedules: An Application of Projective Geometry, Finite Fields, and Graph Theory

Abstract

This paper solves a problem faced by the Suburban East Conference of the Minnesota State High School League in 2009, of designing a consistent wrestling schedule to accommodate a new school. We adapt the application of projective geometry of finite fields to general scheduling problems, and develop an algorithm for determining a schedule. We prove that this algorithm can be completed, will yield the desired schedule, and can yield all possible schedules in the desired format. We also model the schedule with bipartite graphs, and use edge colorings to complete the schedule with home and away assignments.