Maker-Breaker Domination Game

• Maker-Breaker Domination Game is a two-player graph game where players alternately claim vertices aiming to achieve domination.
• The game defines Dominator's win if her set forms a dominating set, while Staller wins by preventing this outcome.
• The game offers insights into combinatorial game theory and graph domination strategies, influencing research on positional game dynamics.

The Maker-Breaker Domination Game is a two-player positional game played on finite graphs, introduced as a specific instance of Maker-Breaker games where the objective is tied to graph domination. The players, Dominator and Staller, alternately claim previously unplayed vertices. Dominator wins if, at any moment, her set of claimed vertices forms a dominating set; Staller wins if Dominator cannot achieve this, equivalently if Staller is able to claim all