论文标题
在具有COP编号4的Girth 7的广义彼得森图上
On Generalised Petersen Graphs of Girth 7 that have Cop Number 4
论文作者
论文摘要
我们表明，如果$ n = 7k/i $带有$ i \ in \ in \ {1,2,3 \} $，则广义Petersen Graph $ GP（N，K）$的COP号为$ 4 $，但一些以前的小例外。以前是Ball等人证明的。 （2015年），任何广义彼得森图的COP数量最多为$ 4 $。本文的结果解释了实际上COP数字$ 4 $但以前没有由Morris等人解释的所有已知的广义Petersen图。在最近的预印本中，将它们置于无限家庭的背景下。 （更确切地说，Morris等人的预印本解释了所有已知的广义Petersen图，带有COP号$ 4 $和Girth $ 8 $，而本文解释了那些拥有Girth $ 7 $的人。）
We show that if $n=7k/i$ with $i \in \{1,2,3\}$ then the cop number of the generalised Petersen graph $GP(n,k)$ is $4$, with some small previously-known exceptions. It was previously proved by Ball et al. (2015) that the cop number of any generalised Petersen graph is at most $4$. The results in this paper explain all of the known generalised Petersen graphs that actually have cop number $4$ but were not previously explained by Morris et al. in a recent preprint, and places them in the context of infinite families. (More precisely, the preprint by Morris et al. explains all known generalised Petersen graphs with cop number $4$ and girth $8$, while this paper explains those that have girth $7$.)
