Enumerative Combinatorics and Postional Games

Abstract

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.