On the Maker-Breaker k-Cycle Game

In this thesis we study the biased Maker-Breaker k-cycle game on the complete graph for a fixed k ∈ N. This is a special case of Maker-Breaker subraph games that are played by two players called Maker and Breaker who alternately claim edges of the complete graph that were previously unclaimed by either player. Maker wins the game if he is able to claim a complete copy of a certain subraph C, which is a k-cycle in the case of Maker-Breaker k-cycle games studied in this thesis. Otherwise Breaker wins. These games are typically played with a bias q ∈ N, meaning that Breaker is allowed to claim up to q edges per turn while Maker only claims one. We give concrete strategies for Breaker for arbitrary k > 3 and for Maker in the case of k ∈ {4,6} that lead to new upper and lower bounds for the bias q.