Biased orientation games
Combinatorics
2011-07-12 v1
Abstract
We study biased {\em orientation games}, in which the board is the complete graph , and Maker and Breaker take turns in directing previously undirected edges of . At the end of the game, the obtained graph is a tournament. Maker wins if the tournament has some property and Breaker wins otherwise. We provide bounds on the bias that is required for a Maker's win and for a Breaker's win in three different games. In the first game Maker wins if the obtained tournament has a cycle. The second game is Hamiltonicity, where Maker wins if the obtained tournament contains a Hamilton cycle. Finally, we consider the -creation game, where Maker wins if the obtained tournament has a copy of some fixed graph .
Cite
@article{arxiv.1107.1844,
title = {Biased orientation games},
author = {Ido Ben-Eliezer and Michael Krivelevich and Benny Sudakov},
journal= {arXiv preprint arXiv:1107.1844},
year = {2011}
}