Geodesic
The game chromatic number of trees and forests
Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 2.

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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. 
@article{DMTCS_2015_17_2_a2,
     author = {Dunn, Charles and Larsen, Victor and Lindke, Kira and Retter, Troy and Toci, Dustin},
     title = {The game chromatic number of trees and forests},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     number = {2},
     year = {2015-2016},
     doi = {10.46298/dmtcs.2130},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2130/}
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Dunn, Charles; Larsen, Victor; Lindke, Kira; Retter, Troy; Toci, Dustin. The game chromatic number of trees and forests. Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 2. doi : 10.46298/dmtcs.2130. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2130/

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