关于确定性僵尸的注记
A note on deterministic zombies
摘要：
“僵尸和幸存者”是一个变种的研究游戏“警察和强盗”，其中僵尸（警察）只能接近幸存者（强盗）。我们考虑游戏的确定性版本，如果有多个选项，僵尸可以选择自己的路径。图中的僵尸数量，就像警察数量一样，是捕获幸存者所需的僵尸或警察的最小数量。在这篇短文中，我们解决了Fitzpatrick等人提出的一个问题，证明了两个图的笛卡儿积的僵尸数至多是它们的僵尸数之和。我们还给出了一个单图族，它的cop数为$2$，僵尸数为任意大。
英文摘要：
"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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
