Contributions to Maker-Breaker GameDokyeesun, Pakanun (Avtor) Klavžar, Sandi (Mentor) Bujtás, Csilla (Komentor) Maker-Breaker gameMaker-Breaker domination gamemonochromatic clique transversal gameThe framework of the dissertation is the theory of the Maker-Breaker game, a game being played by two players, Maker and Breaker, on a hypergraph ${\cal H}$. The vertex set of ${\cal H}$ is the board of the game, while the hyperedges are winning sets. The two players take turns to choose an unplayed vertex from the board. Due to the great generality of hypergraphs, the winning sets can be defined such that they reflect many different situations. For this reason, too, the game was developed and extensively studied in the last decades and is an appealing topic of modern combinatorics. In the most studied variants of the game, the winning sets represent some vertex or edge sets of a graph with specified properties. In this thesis, we focus on the Maker-Breaker domination game (MBD game) and biased Maker-Breaker game, especially the biased monochromatic clique transversal game (MCT game). In these versions, the players are named Dominator and Staller. We define the winning number of the players, respectively, and establish some general related results for the Maker-Breaker game. We discuss similarities and differences of the Maker-Breaker domination game from Dominator's and Staller's points of view and determine fast winning strategies for both players. We also introduce the SMBD-number, which is the minimum number of moves Staller needs to win, and prove some general properties, including the relation between SMBD-numbers and the minimum degree of a graph. Then, we explore the MBD game on trees and present a characterization for trees with SMBD-number $k$, for every positive integer $k$. Exact formulas for paths, caterpillars, tadpole graphs, and most of the subdivided stars are also determined. Furthermore, we investigate the outcome of the MBD game on Cartesian products of paths and cycles, of complete bipartite graphs, and provide a fast winning strategy for the winner of the game. For the $(a,b)$-MCT game, we determine thresholds for triangle-free graphs, bounds for thresholds for disjoint union of graphs, and thresholds for Cartesian products of paths and cycles.20242024-05-29 08:15:03Doktorsko delo/naloga158192UDK: 519.17VisID: 139804COBISS_ID: 197056771sl