A note on the connected game coloring number
Combinatorics
2020-06-16 v2
Abstract
We consider the \emph{connected game coloring number} of a graph, introduced by Charpentier et al. as a game theoretic graph parameter that measures the degeneracy of a graph with respect to a certain two-player game played with an uncooperative adversary. We consider the connected game coloring number of graphs of bounded treedepth and of -trees. In particular, we show that there exists an outerplanar -tree with connected game coloring number of , which answers a question from [C. Charpentier, H. Hocquard, E. Sopena, and X. Zhu. A connected version of the graph coloring game. \textit{Discrete Appl. Math.}, 2020].
Cite
@article{arxiv.2006.03188,
title = {A note on the connected game coloring number},
author = {Peter Bradshaw},
journal= {arXiv preprint arXiv:2006.03188},
year = {2020}
}
Comments
7 pages