Avoider-Enforcer star games

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 jr is the hypergraph of the game.