Abstract
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 6 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 Kt-minor game.
Original language | English |
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Pages (from-to) | 194-212 |
Number of pages | 19 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 22 |
Issue number | 1 |
DOIs | |
State | Published - 2008 |
Keywords
- Combinatorial games
- Graph coloring
- Graph minors
- Planar graph