Hosseini, Seyyed Aliasghar ; Mohar, Bojan, 1956- ; González Hermosillo de la Maza, Sebastián
The game of Cops and Robbers is a well known pursuit-evasion game played on graphs. It has been proved \cite{bounded_degree} that cubic graphs can have arbitrarily large cop number ▫$c(G)$▫, but the ...known constructions show only that the set ▫$\{c(G) \mid G \text{ cubic}\}$▫ is unbounded. In this paper we prove that there are arbitrarily large subcubic graphs ▫$G$▫ whose cop number is at least ▫$n^{1/2-o(1)}$▫ where ▫$n=|V(G)|$▫. We also show that proving Meyniel's conjecture for graphs of bounded degree implies a weak Meyniel's conjecture for all graphs.
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