Planarity, Colorability, and Minor Games
Dan Hefetz, Michael Krivelevich, Miloš Stojaković, Tibor Szabó · SIAM Journal on Discrete Mathematics · 2008
Let m 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 of 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 of 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 $K_t$-minor game.