Andrzej Grzesik (1), Mirjana Mikalački (2), Zoltán Lóránt Nagy (3), Alon Naor (4), Balázs Patkós (5) (3), Fiona Skerman (6)
(1) Theoretical Computer Science Department [Krakow]
(2) Department of Mathematics and Informatics [Novi Sad]
(3) Alfréd Rényi Institute of Mathematics
(4) School of Mathematical Sciences [Tel Aviv]
(5) Geometric and Algebraic Combinatorics Research Group
(6) Department of Statistics [Oxford]
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 fmonF, f-F and f+F, where F is the hypergraph of the game.
