(2017-04) Spessard, Clark; Whieldon, Gwyneth; Hood College Mathematics; Hood College Departmental Honors
Graph Avoidance games are a commonly studied type of combinatorial game. One class of graph avoidance games are Maker-Breaker games (Definition 3.4.1). In this thesis we prove weak solutions to Maker-Breaker games where Maker must construct a cycle, which we call Cycle Games (Definition 3.4.2), as well as provide methods to reduce the size of Cycle Game trees.