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arXiv · 1302.2555

Avoider-Enforcer star games

Andrzej Grzesik·Mirjana Mikalački·Zoltán Lóránt Nagy·Alon Naor·Balázs Patkós·Fiona Skerman
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Abstract

In this paper, we study $(1 : b)$ Avoider-Enforcer games played on the edge set of the complete graph on $n$ vertices. For every constant $k\geq 3$ we analyse the $k$-star game, where Avoider tries to avoid claiming $k$ edges incident to the same vertex. We analyse both versions of Avoider-Enforcer games -- the strict and the monotone -- and for each provide explicit winning strategies for both players. We determine the order of magnitude of the threshold biases $f^{mon}_\mathcal{F}$, $f^-_\mathcal{F}$ and $f^+_\mathcal{F}$, where $\mathcal{F}$ is the hypergraph of the game.

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Andrzej Grzesik, Mirjana Mikalački, Zoltán Lóránt Nagy, Alon Naor, Balázs Patkós, Fiona Skerman. 2013-02-11. Avoider-Enforcer star games. https://arxiv.org/abs/1302.2555

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