  While the game chromatic number of a forest is known to be at most 4, no
simple criteria are known for determining the game chromatic number of a
forest. We first state necessary and sufficient conditions for forests with
game chromatic number 2 and then investigate the differences between forests
with game chromatic number 3 and 4. In doing so, we present a minimal example
of a forest with game chromatic number 4, criteria for determining the game
chromatic number of a forest without vertices of degree 3, and an example of a
forest with maximum degree 3 and game chromatic number 4.
