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Journal Articles Discrete Mathematics Year : 2020

Maker-Breaker domination game

Eric Duchene
Valentin Gledel
Aline Parreau


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.
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hal-01848805 , version 1 (25-07-2018)



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⟩
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