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arXiv · 1807.09479

Maker-Breaker domination game

Eric Duchêne·Valentin Gledel·Aline Parreau·Gabriel Renault
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Abstract

We introduce the Maker-Breaker domination game, a two player game on a graph. At his turn, the first 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 first 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 define 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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Eric Duchêne, Valentin Gledel, Aline Parreau, Gabriel Renault. 2018-07-25. Maker-Breaker domination game. https://arxiv.org/abs/1807.09479

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