Fast winning strategies in Avoider-Enforcer games

Details Fast winning strategies in Avoider-Enforcer games Fast winning strategies in Avoider-Enforcer games

2008-06-02

arxiv.org/abs/0806.0280v1

Mathematics

Combinatorics

Scientific paper

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type 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 $K_n$ 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.

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