# A note on the connected game coloring number

@article{Bradshaw2020ANO, title={A note on the connected game coloring number}, author={Peter Bradshaw}, journal={arXiv: Combinatorics}, year={2020} }

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 $k$-trees. In particular, we show that there exists an outerplanar $2$-tree with connected game coloring number of $5$, which answers a question from [C…

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