• DOI:10.11575/CDM.V12I2.62508
• Corpus ID: 31441516

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}
}

• D. Cardoso, C. Dominic, +1 author M. Witkowski
• 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 $c(G^{\Xi})\leq 3$. Furthermore we investigate the cop-edge critical graphs, i.e. graphs that for any edge $e$ in $G$ we have either $c(G-e) c(G)$. We show couple examples of cop-edge critical graphs having cop number equal to~$3$.