All Questions

Let $G = (V, E)$ be a finite graph, and $S \subseteq V$ initially be an empty set. Alice and Bob play a game, making moves in turns starting with Alice. A move consists of choosing a vertex $v \in V \...

Let $\mathfrak{G}$ be the class of all finite directed and undirected graphs. Let $A,B\subseteq \mathfrak{G} $, $A$ and $B$ are closed under graph isomorphisms, and $A \cap B = \varnothing$. Consider ...