论文标题
确定性僵尸的注释
A note on deterministic zombies
论文作者
论文摘要
“僵尸和幸存者”是研究精彩的“警察和强盗”游戏的变体，僵尸（警察）只能更靠近幸存者（强盗）。我们考虑游戏的确定性版本，如果有多个选项可用，僵尸可以选择其路径。图形的僵尸编号（例如COP）是捕获幸存者所需的僵尸数量的最小数量或COP。在此简短的说明中，我们解决了Fitzpatrick等人的一个问题，证明了两个图的笛卡尔产品的僵尸数量最多是其僵尸数字的总和。我们还提供了一个简单的图形系列，其中COP号$ 2 $和一个任意大的僵尸编号。
"Zombies and Survivor" is a variant of the well-studied game of "Cops and Robber" where the zombies (cops) can only move closer to the survivor (robber). We consider the deterministic version of the game where a zombie can choose their path if multiple options are available. The zombie number, like the cop number, of a graph is the minimum number of zombies, or cops, required to capture the survivor. In this short note, we solve a question by Fitzpatrick et al., proving that the zombie number of the Cartesian product of two graphs is at most the sum of their zombie numbers. We also give a simple graph family with cop number $2$ and an arbitrarily large zombie number.
