A note on the connected game coloring number

We consider the 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 connected version of the graph marking game. We establish bounds for the connected game coloring number of graphs of bounded treedepth and of k-trees. We also show that there exists an outerplanar 2-tree with connected game coloring number 5, which answers a question from Charpentier et al., (2020).(c) 2023 Elsevier B.V. All rights reserved.