English

The game chromatic number of trees and forests

Combinatorics 2014-10-21 v1

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.

Keywords

Cite

@article{arxiv.1410.5223,
  title  = {The game chromatic number of trees and forests},
  author = {Charles Dunn and Victor Larsen and Kira Lindke and Troy Retter and Dustin Toci},
  journal= {arXiv preprint arXiv:1410.5223},
  year   = {2014}
}

Comments

18 pages, 15 figures, submitted