Keeping Avoider’s graph almost acyclic

Publikationstyp
Journal Article
Date Issued
2015-03-06
Sprache
English
Author(s)
Clemens, Dennis  orcid-logo
Ehrenmüller, Julia  
Person, Yury  
Tran, Tuan  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/10042
Journal
The electronic journal of combinatorics  
Volume
22
Issue
1
Start Page
1
End Page
12
Article Number
P1.60
Citation
Electronic Journal of Combinatorics 22 (1): P1.60, 1-12 (2015-03-06)
Publisher DOI
10.37236/4859
Scopus ID
2-s2.0-84924236083
Publisher
EMIS ELibEMS
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 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.
Subjects
Avoider-Enforcer
Planarity game
Positional games
Threshold bias
DDC Class
510: Mathematik