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Maker-Breaker domination game

Abstract : 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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Submitted on : Wednesday, July 25, 2018 - 11:08:48 AM
Last modification on : Saturday, June 25, 2022 - 10:38:34 AM
Long-term archiving on: : Friday, October 26, 2018 - 1:55:02 PM


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  • HAL Id : hal-01848805, version 1


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



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