  This paper introduced a pursuit and evasion game to be played on a connected
graph. One player moves invisibly around the graph, and the other player must
guess his position. At each time step the second player guesses a vertex,
winning if it is the current location of the first player; if not the first
player must move along an edge. It is shown that the graphs on which the second
player can guarantee to win are precisely the trees that do not contain a
particular forbidden subgraph, and best possible capture times on such graphs
are obtained.
