  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.
