Maker–Breaker domination game

We introduce the Maker–Breaker domination game, a two player game on a graph. At his turn, the first player, Dominator, selects 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 alternat...

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Bibliographic Details
Published inDiscrete mathematics Vol. 343; no. 9; p. 111955
Main Authors Duchêne, Eric, Gledel, Valentin, Parreau, Aline, Renault, Gabriel
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2020
Elsevier
Subjects
Cograph
Combinatorics
Complexity
Computer Science
Discrete Mathematics
Domination game
Maker–Breaker domination game
Mathematics
Positional games
Tree
Tree
Maker–Breaker domination game
Cograph
Positional games
Domination game
Complexity
tree
complexity
cograph
positional games
Maker-Breaker domination game
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Summary:We introduce the Maker–Breaker domination game, a two player game on a graph. At his turn, the first player, Dominator, selects 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.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.111955