Nathan J. Bowler

Maker-Breaker games on infinite graphs with precolored edges

Suppose we are given graphs $B$ and $G$. In the classical Maker-Breaker game $\text{MB}(B,G)$ two players, Maker and Breaker, alternately claim edges of $B$ and it is Maker's goal to claim a copy of $G$ in $B$, while it is Breaker's goal to prevent that. In this paper, $B$ is the countably infinite complete graph $K_{\...