Clemens, DennisDennisClemensEhrenmüller, JuliaJuliaEhrenmüllerPerson, YuryYuryPersonTran, TuanTuanTran2021-08-042021-08-042015-03-06Electronic Journal of Combinatorics 22 (1): P1.60, 1-12 (2015-03-06)http://hdl.handle.net/11420/10042We consider biased (1:b) 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 b ²00nlnn. By this we obtain essentially optimal upper bounds on the threshold biases for the non-planarity game, the non-k-colorability game, and the K-minor game thus addressing a question and improving the results of Hefetz, Krivelevich, Stojakovic, and Szabo. Moreover, we give a slight improvement for the lower bound in the non-planarity game.en1077-892620151112EMIS ELibEMSAvoider-EnforcerPlanarity gamePositional gamesThreshold biasMathematikJournal Article10.37236/4859Other