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The domination game is played on a graph G by two players, Dominator and Staller, who alternate in selecting vertices until each vertex in the graph G is contained in the closed neighbourhood of the set of selected vertices. Dominator's aim is to reach this state in as few moves as possible, whereas Staller wants the game to last as long as possible. In this paper, we prove that if G has n vertices and minimum degree at least 2, then Dominator has a strategy to finish the domination game on G within 10n/17+1/17 moves, thus making progress towards a conjecture by Bujtás, Iršič and Klavžar.
Portier et al. (Tue,) studied this question.