Maker–Breaker total domination game on cubic graphs
We study Maker–Breaker total domination game played by two players, Dominator and Staller, on the connected cubic graphs. Staller (playing the role of Maker) wins if she manages to claim an open neighbourhood of a vertex. Dominator wins otherwise (i.e. if he can claim a total dominating set of a graph). For certain graphs on n 6 vertices, we give the characterization on those which are Dominator’s win and those which are Staller’s win.
Positional games, Maker–Breaker game, Total domination game, Cubic graphs, Generalized Petersen graph