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

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 3 n / 5 moves, which was conjectured by Kinnersley, West and Zamani.