### Avoider-Enforcer star games

*Andrzej Grzesik, Mirjana Mikalacki, Zoltan Lorant Nagy, Alon Naor, Balazs Patkos, Fiona Skerman*

#### 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≥3 we analyse the
k-star game, where Avoider tries to avoid claiming
k edges incident to the same vertex. We consider 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}_{F}, f^{-}_{F}and f^{+}_{F}, where F is the hypergraph of the game.Full Text: PDF PostScript