• Corpus ID: 219402254

A note on the connected game coloring number

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