Avoider-Enforcer games

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not who wins but rather how fast can one win. These types of problems were studied earlier for Maker-Breaker games; here we initiate their study for unbiased Avoider-Enforcer games played on the edge set of the complete graph Kn on n vertices. For several games that are known to be an Enforcer’s win, we estimate quite precisely the minimum number of moves Enforcer has to play in order to win. We consider the non-planarity game, the connectivity game and the non-bipartite game.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Dan Hefetz, Michael Krivelevich, Tibor Szabó
• Keywords: Complete Graph Kn, JCT 2007, Numerous Positional Games, Unbiased Avoider-enforcer Games