# 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}
}
• Published 27 November 2017
• Mathematics
• Contributions Discret. Math.
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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