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.

翻译：Cops 和 Robbers 的游戏是在图表上玩的众所周知的追逐- 规避游戏。 事实证明, 立方图可以任意设定大号的警察, 美元( G) $( G), 但已知的构造仅显示, 设定的 $c( G)\ mid G\ text { 立方 $( 立方 ) 不受约束 。 在本文中, 我们证明有任意大型的亚立方图 $G$, 其警察人数至少是$n ⁇ 1/2- o(1)} $( 美元) 。 我们还显示, 证明 Meyniel 的定界图的推测意味着 Meyniel 对所有图表的猜测力很弱 。