# On Cops and Robbers on $G^{\Xi}$ and cop-edge critical graphs

@article{Cardoso2017OnCA, title={On Cops and Robbers on \$G^\{\Xi\}\$ and cop-edge critical graphs}, author={Domingos Moreira Cardoso and Charles Dominic and Lukas T. Witkowski and Marcin Witkowski}, journal={Contributions Discret. Math.}, year={2017}, volume={12} }

Cop Robber game is a two player game played on an undirected graph. In this game cops try to capture a robber moving on the vertices of the graph. The cop number of a graph is the least number of cops needed to guarantee that the robber will be caught. In this paper we presents results concerning games on $G^{\Xi}$, that is the graph obtained by connecting the corresponding vertices in $G$ and its complement $\overline{G}$. In particular we show that for planar graphs $c(G^{\Xi})\leq 3…

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