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arXiv · 2306.05728

The Maker-Maker domination game in forests

Eric Duchêne·Arthur Dumas·Nacim Oijid·Aline Parreau·Eric Rémila
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Abstract

We study the Maker-Maker version of the domination game introduced in 2018 by Duchêne et al. Given a graph, two players alternately claim vertices. The first player to claim a dominating set of the graph wins. As the Maker-Breaker version, this game is PSPACE-complete on split and bipartite graphs. Our main result is a linear time algorithm to solve this game in forests. We also give a characterization of the cycles where the first player has a winning strategy.

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Eric Duchêne, Arthur Dumas, Nacim Oijid, Aline Parreau, Eric Rémila. 2023-06-09. The Maker-Maker domination game in forests. https://arxiv.org/abs/2306.05728

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