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arXiv · 1410.5223

The game chromatic number of trees and forests

Charles Dunn·Victor Larsen·Kira Lindke·Troy Retter·Dustin Toci
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Abstract

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.

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Charles Dunn, Victor Larsen, Kira Lindke, Troy Retter, Dustin Toci. 2014-10-20. The game chromatic number of trees and forests. https://arxiv.org/abs/1410.5223

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