Maker-Breaker games on $K_{{\omega }_1}$ and $K_{\omega ,{\omega }_1}$

Nathan Bowler, Florian Gut, Attila Joó +1

We investigate Maker-Breaker games on graphs of size ${\aleph }_1$ in which Maker's goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the gam…