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We analyze the domination game, where two players, Dominator and Staller,construct together a dominating set M in a given graph, by alternatelyselecting vertices into M. Each move must increase the size of the dominatedset. The players have opposing goals: Dominator wishes M to be as small aspossible, and Staller has the opposite goal. Kinnersley, West and Zamaniconjectured that when both players play optimally on an isolate-free forest,there is a guaranteed upper bound for the size of the dominating set thatdepends only on the size n of the forest. This bound is 3n/5 when the firstplayer is Dominator, and (3n+2)/5 when the first player is Staller. Theconjecture was proved for specific families of forests by Kinnersley et al. andlater extended by Bujtas. Here we prove it for all isolate-free forests, bysupplying an algorithm for Dominator that guarantees the desired bound.

The Domination Game: Proving the 3/5 Conjecture on Isolate-Free Forests