Planarity, Colorability, and Minor Games

Letm and b be positive integers and let F be a hypergraph. In an (m, b) Maker-Breaker game F two players, called Maker and Breaker, take turns selecting previously unclaimed vertices of F . Maker selects m vertices per move and Breaker selects b vertices per move. The game ends when every vertex has been claimed by one of the players. Maker wins if he claims all the vertices of some hyperedge of F ; otherwise Breaker wins. An (m, b) Avoider-Enforcer game F is played in a similar way. The only difference is in the determination of the winner: Avoider loses if he claims all the vertices of some hyperedge of F ; otherwise Enforcer loses. In this paper we consider the Maker-Breaker and Avoider-Enforcer versions of the planarity game, the k-colorability game and the Kt-minor game.