Maker-Breaker total domination games on cubic graphs
Jovana Forcan, Mirjana Mikalački · arXiv (Cornell University) · 2020
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 $n\geq 6$ vertices, we give the characterization on those which are Dominator's win and those which are Staller's win.