Fast winning strategies in positional games

Abstract

For the unbiased Maker-Breaker game, played on the hypergraph H, let τM (H) be the smallest integer t such that Maker can win the game within t moves (if the game is a Breaker's win, then set τM (H) = ∞). Similarly, for the unbiased Avoider-Enforcer game played on H, let τE (H) be the smallest integer t such that Enforcer can win the game within t moves (if the game is an Avoider's win, then set τM (E) = ∞). We investigate τM and τE and determine their value for various positional games. © 2007 Elsevier B.V. All rights reserved.