Maker-Breaker on Galton-Watson trees
We consider the following combinatorial two-player game: On the random tree arising from a branching process, each round one player (Breaker) deletes an edge and by that removes the descendant and all its progeny, while the other (Maker) fixates an edge to permanently secure it from deletion. Breaker has won once the tree's root is contained in a finite component, otherwise Maker wins by building We consider the following combinatorial two-player game: On the random tree arising from a branching process, each round one player (Breaker) deletes an edge and by that removes the descendant and all its progeny, while the other (Maker) fixates an edge to permanently secure it from deletion. Breaker has won once the tree's root is contained in a finite component, otherwise Maker wins by building