Authors: Jovana Forcan ; Mirjana Mikalački

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.

• 05C57 - Games on graphs (graph-theoretic aspects)
• 05C69 - Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
• 91A05 - 2-person games
• 91A43 - Games involving graphs