Abstract
The domination game belongs to the growing family of competitive optimization graph games, and describes a process in which two players, Dominator and Staller, take turns choosing a vertex from a graph G. Each vertex chosen must dominate at least one vertex not dominated by the set of vertices previously chosen. The game ends when there are no more moves available. The players have conflicting goals: while Dominator wants to minimize the size of a dominating set, Staller wants to maximize it. In this chapter, we present selected results on three domination-type game parameters, namely the domination game, the total domination game, and the independent domination game.
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