Fast winning strategies in positional games

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 τE(H) = ∞). In this paper, we investigate τM and τE and determine their value for various positional games.

• Type: Journal
• Year: 2007
• Where: ENDM
• Authors: Dan Hefetz, Michael Krivelevich, Milos Stojakovic, Tibor Szabó
• Keywords: ENDM 2007, Game, Smallest Integer, Unbiased Maker-breaker Game