This question is motivated by a board game called 'Dracula'. In this game there is one vampire and four hunters, the purpose of the hunters is to catch the vampire. The game takes place in Europe. The game looks as follows:
1. The hunter player puts all hunters in cities. More than one hunter can be placed in the same city.
2. The vampire player puts the vampire in a city.
3. Players alternately move their creatures to the neighboring cities.
4. The hunter player in his turn may move as many hunters as he wants.
5. The main difficulty is that the vampire player knows all the time where the hunters are, but the hunter player knows only the starting position of the vampire.
6. When a hunter and the vampire meets in a city then the vampire player loses.
For a given graph $G$ and numbers $n$ and $k$, is there a strategy that guarantees the hunter player, who controls $n$ hunters, to catch vampire in less than $k$ turns? It may be assumed that $G$ is planar. Has this problem been studied? Some references would be appreciated.