[1]This game remained a well-known open problem until it was solved by Shmuel Gal in the late 1970s.
This game has been solved by Steve Alpern and independently by Mikhail Zelikin only for the very simple graph consisting of a single loop (a circle).
[6][7] The value of the game on the unit interval (a graph with two nodes with a link in-between) has been estimated approximatively.
The obvious search strategy of starting at a random end and "sweeping" the whole interval as fast as possible guarantees a 0.75 expected capture time, and is not optimal.
By utilizing a more sophisticated mixed searcher and hider strategy, one can reduce the expected capture time by about 8.6%.