Maker-Breaker domination game
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.
Keywords
Cite
@article{arxiv.1807.09479,
title = {Maker-Breaker domination game},
author = {Eric Duchêne and Valentin Gledel and Aline Parreau and Gabriel Renault},
journal= {arXiv preprint arXiv:1807.09479},
year = {2018}
}