We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the zombies that play the role of the cops. The zombies are restricted, on their turn, to always follow an edge of a shortest path towards the survivor. Let $z(G)$ be the smallest number of zombies required to catch the survivor on a graph $G$ with $n$ vertices. We show that there exist outerplanar graphs and visibility graphs of simple polygons such that $z(G) = \Theta(n)$. We also show that there exist maximum-degree-$3$ outerplanar graphs such that $z(G) = \Omega\left(n/\log(n)\right)$. Let $z_L(G)$ be the smallest number of lazy zombies (zombies that can stay still on their turn) required to catch the survivor on a graph $G$. We establish that lazy zombies are more powerful than normal zombies but less powerful than cops. We prove that $z_L(G) = 2$ for connected outerplanar graphs. We show that $z_L(G)\leq k$ for connected graphs with treedepth $k$. This result implies that $z_L(G)$ is at most $(k+1)\log n$ for connected graphs with treewidth $k$, $O(\sqrt{n})$ for connected planar graphs, $O(\sqrt{gn})$ for connected graphs with genus $g$ and $O(h\sqrt{hn})$ for connected graphs with any excluded $h$-vertex minor. Our results on lazy zombies still hold when an adversary chooses the initial positions of the zombies.

翻译：我们研究僵尸和幸存者,这是警察游戏和强盗游戏的变体。在这个变体中,独生者扮演强盗的角色,试图逃离充当警察角色的僵尸。僵尸被限制在通往幸存者的最短路径的边缘。让z(G)$(G)成为在一张图上用$n元的悬念捕获幸存者所需的最小僵尸数量。我们显示,存在外部平面图和简单多边形的可见度图,例如,z(G)$=\Theta(n)美元。我们还显示,有最高度-度-3美元的外平面图,因此,z(G)==Omegaleft(n/q(n)\q(right)$。让z_(G)成为最小的懒惰性僵尸(Z)数字(可以保持在转基因值的平面图上)的最小数量。我们确认,在数字上,懒制的僵尸数量比正常的平面的平面值要强。