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While the game chromatic number of a forest is known to be at most 4, nosimple criteria are known for determining the game chromatic number of aforest. We first state necessary and sufficient conditions for forests withgame chromatic number 2 and then investigate the differences between forestswith game chromatic number 3 and 4. In doing so, we present a minimal exampleof a forest with game chromatic number 4, criteria for determining the gamechromatic number of a forest without vertices of degree 3, and an example of aforest with maximum degree 3 and game chromatic number 4.

The game chromatic number of trees and forests