Maker-Breaker domination game

Eric Duchene (1) , Valentin Gledel (1) , Aline Parreau (1) , Gabriel Renault (2)

1 GOAL - Graphes, AlgOrithmes et AppLications
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We introduce the Maker-Breaker domination game, a two player game on a graph. At his turn, the rst player, Dominator, select a vertex in order to dominate the graph while the other player, Staller, forbids a vertex to Dominator in order to prevent him to reach his goal. Both players play alternately without missing their turn. This game is a particular instance of the so-called Maker-Breaker games, that is studied here in a combinatorial context. In this paper, we rst prove that deciding the winner of the Maker-Breaker domination game is PSPACE-complete, even for bipartite graphs and split graphs. It is then showed that the problem is polynomial for cographs and trees. In particular, we dene a strategy for Dominator that is derived from a variation of the dominating set problem, called the pairing dominating set problem.

Mots clés: positional games; Maker-Breaker domination game; Domination game; complexity; tree; cograph

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Eric Duchene, Valentin Gledel, Aline Parreau, Gabriel Renault. Maker-Breaker domination game. Discrete Mathematics, 2020, 343 (9), ⟨10.1016/j.disc.2020.111955⟩. ⟨hal-01848805⟩