Authors: Charles Dunn ¹; Victor Larsen ²; Kira Lindke ³; Troy Retter ⁴; Dustin Toci ⁵

• 1 Linfield College
• 2 Kennesaw State University
• 3 Michigan Technological University
• 4 Emory University [Atlanta, GA]
• 5 Auteur indépendant

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 in polynomial time 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. This gives partial progress on the open question of the computational complexity of the game chromatic number of a forest.