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arXiv · 2212.04527

A proof of the 3/5-conjecture in the domination game

Leo Versteegen
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Abstract

The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each selected vertex must strictly increase the number of dominated vertices at the time of its selection, and the game ends once every vertex in $G$ is dominated. Dominator aims to keep the game as short as possible, while Staller tries to achieve the opposite. In this article, we prove that for any graph $G$ on $n$ vertices, Dominator has a strategy to end the game in at most $3n/5$ moves, which was conjectured by Kinnersley, West and Zamani.

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Leo Versteegen. 2022-12-08. A proof of the 3/5-conjecture in the domination game. https://arxiv.org/abs/2212.04527

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