English

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 kk-trees. In particular, we show that there exists an outerplanar 22-tree with connected game coloring number of 55, 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].

Keywords

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

R2 v1 2026-06-23T16:04:24.542Z