Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
In this thesis we study different kinds of combinatorial games between two players, which are played on a board that consists of the edges of some given graph G. We distinguish unbiased games, in which both players claim/orient one edge in each round, and b-biased games in which the second player claims/orients b edges in each round. The first game in this regard is the strict oriented-cycle game, which was introduced by Bollobás and Szabó, and later studied by Ben-Eliezer, Krivelevich and Sudakov. It is played by OMaker and OBreaker, who assign orientations to the edges of the complete graph K_n alternately. OMaker has the goal to create a directed cycle, while OBreaker wants to prevent such. It has been asked by Bollobás and Szabó to find the largest value b for which OMaker has a winning strategy in the b-biased strict oriented-cycle game, i.e. when OBreaker orients b edges in each round. They conjectured this value to be n-3, which turned out to be false, when, in an earlier work with Liebenau, we were able to show an upper bound of size n-c\sqrt{n}. In this thesis we improve on this bound, and we show that even for b> 37n/40 OBreaker has a strategy to prevent cycles. The second game is the tournament game, which was introduced by Beck. Here, TMaker and TBreaker, alternately claim edges of a given graph G, where TMaker additionally assigns orientations to her edges. She wins, if her directed graph contains at least one copy of a pre-defined tournament T, while TBreaker wins otherwise. We consider this game when G is the complete graph K_n or a random graph sampled according to the random graph model G_{n,p}, whereas T is a tournament on a constant number k of vertices. We study thresholds for the bias b and the probability p around which a TMaker's win suddenly turns into a TBreaker's win. As third, we study the tree embedding game, which belongs to the family of Maker-Breaker games. The latter became very popular throughout the last decades, as many researchers, including Beck, Bednarska, Erdös, Hefetz, ...