In this paper we study the (a : b) Maker-Breaker Connectivity game, played on the edge set of the complete graph on n vertices. We determine the winner for almost all values of a and b.
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 analyse both versions of Avoider-Enforcer games – the strict and the monotone – and for each provide explicit… (More)
We study the Maker-Breaker tournament game played on the edge set of a given graph G. Two players, Maker and Breaker, claim unclaimed edges of G in turns, while Maker additionally assigns orientations to the edges that she claims. If by the end of the game Maker claims all the edges of a pre-defined goal tournament, she wins the game. Given a tournament T k… (More)
We study the (a : a) Maker-Breaker games played on the edge set of the complete graph on n vertices. In the following four games – perfect matching game, Hamil-tonicity game, star factor game and path factor game, our goal is to determine the least number of moves which Maker needs in order to win these games. Moreover, for all games except for the star… (More)