Keeping Avoider's graph almost acyclic [article]

Dennis Clemens, Julia Ehrenmüller, Yury Person, Tuan Tran
2014 arXiv   pre-print
We 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 ≥ 200 n n. 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_t-minor game thus addressing a question and improving the results of Hefetz, Krivelevich, Stojaković, and Szabó. Moreover, we give a slight
more » ... improvement for the lower bound in the non-planarity game.
arXiv:1403.1482v1 fatcat:6q2xe4szuffy3ptzinvbrq4riu