The Maker–Maker domination game in forests

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....

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Published inDiscrete Applied Mathematics Vol. 348; pp. 6 - 34
Main Authors Duchêne, Eric, Dumas, Arthur, Oijid, Nacim, Parreau, Aline, Rémila, Eric
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.05.2024
Elsevier
Subjects
Combinatorics
Computational Complexity
Computer Science
Dominating set
Domination game
Graphs
Maker–Breaker games
Maker–Maker games
Mathematics
Positional games
PSPACE-completeness
Maker–Breaker games
Dominating set
Maker–Maker games
PSPACE-completeness
Graphs
Positional games
Domination game
Maker-Maker Games
Positional Games
Maker-Breaker Games
domination game
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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.
AbstractList 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.
Author Oijid, Nacim
Rémila, Eric
Duchêne, Eric
Parreau, Aline
Dumas, Arthur
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  organization: Univ. of Lyon, UJM Saint-Etienne, GATE UMR CNRS 5824, F-42023, Saint-Etienne, France
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Keywords Maker–Breaker games
Dominating set
Maker–Maker games
PSPACE-completeness
Graphs
Positional games
Domination game
Maker-Maker Games
Positional Games
Maker-Breaker Games
domination game
Language English
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Snippet 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...
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...
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SubjectTerms Combinatorics
Computational Complexity
Computer Science
Dominating set
Domination game
Graphs
Maker–Breaker games
Maker–Maker games
Mathematics
Positional games
PSPACE-completeness
Title The Maker–Maker domination game in forests
URI https://dx.doi.org/10.1016/j.dam.2024.01.023
https://hal.science/hal-04123172
Volume 348
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