论文标题
有关连接的游戏颜色编号的注释
A note on the connected game coloring number
论文作者
论文摘要
我们考虑了Charpentier等人介绍的图的\ emph {连接的游戏颜色}。作为游戏理论图参数，可以根据某个具有不合作对手的两种玩家游戏来衡量图形的变性。我们考虑连接的游戏着色编号和$ k $树的有限图形的图形。特别是，我们表明存在一个外套$ 2 $ -tree，带有连接的游戏着色$ 5 $，它回答了[C. C. Charpentier，H。Hocquard，E。Sopena和X. Zhu。图形着色游戏的连接版本。 \ textIt {iNCETE APPL。数学。}，2020年]。
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. Charpentier, H. Hocquard, E. Sopena, and X. Zhu. A connected version of the graph coloring game. \textit{Discrete Appl. Math.}, 2020].
