1 research outputs found
Keeping Avoider's graph almost acyclic
We consider biased Avoider-Enforcer games in the monotone and strict
versions. In particular, we show that Avoider can keep his graph being a forest
for every but maybe the last round of the game if . By this
we obtain essentially optimal upper bounds on the threshold biases for the
non-planarity game, the non--colorability game, and the -minor game
thus addressing a question and improving the results of Hefetz, Krivelevich,
Stojakovi\'c, and Szab\'o. Moreover, we give a slight improvement for the lower
bound in the non-planarity game.Comment: 11 page