KöMaL 2024 B5412

A fugitive at a vertex of a finite connected graph is being chased by three policemen at three other vertices. First the fugitive makes a move along an edge, then each of the three policemen can also make a move along an edge. The game continues by alternating turns between the fugitive and the policemen. Can the policemen always catch the fugitive in a finite number of steps, i.e., can they always guarantee that one of them will be on the same vertex as the fugitive after a finite number of steps?