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arXiv · 1107.1844

Biased orientation games

Ido Ben-Eliezer·Michael Krivelevich·Benny Sudakov
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Abstract

We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker wins if the tournament has some property $\mathcal P$ 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 $H$-creation game, where Maker wins if the obtained tournament has a copy of some fixed graph $H$.

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Ido Ben-Eliezer, Michael Krivelevich, Benny Sudakov. 2011-07-10. Biased orientation games. https://arxiv.org/abs/1107.1844

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