Discrete Mathematics & Theoretical Computer Science, Vol 17, No 1 (2015)

Font Size:  Small  Medium  Large

Avoider-Enforcer star games

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


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.

Full Text: PDF PostScript