From: "David Wilson" <davidwwilson@comcast.net>

Each edge is a corridor, each vertex a circular room. Corridors enter at doors in fixed positions around the room, so that you can tell which corridor is left or right of another with respect to the vertex.

From: Fred lunnon <fred.lunnon@gmail.com>

It's a very nice problem --- tho' I can't help wondering if it's already been tackled --- by Erdos et al, perhaps?

Don't know the Erdos number, but in season 4, episode 23, "The House That Jack Built", of _The Avengers_ TV show, which is just about the best episode of any TV show EVAH, Emma Peel tackled the problem in a different way. ======== SPOILERS ========= Weep dorp. Humm humm humm.... Wa-deep dorp. Humm humm humm.... Weep dorp. Humm humm humm.... Wa-deep dorp. Humm humm humm.... Weep dorp. Humm humm humm.... Wa-deep dorp. Humm humm humm.... Weep dorp. Humm humm humm.... Wa-deep dorp. Humm humm humm.... After a bit of frantic maze-running, Mrs. Peel cooled her heels and drew a lipstick X on the clear cover of the creepy beeping machine in the center of the circular room. When she got to the room at the end of the first corridor, there was the X. This led her to realize (before punching through a wall and showing us the audience) that the corridor was on a track so that either end could be automatically wheeled around to the room, producing a crazy- making virtual infinite lattice effect. Of course the resourceful Mrs. Peel is not so easily driven crazy, rather the point of the episode. http://theavengers.tv/forever/peel1-23.htm Thumbnail of the room: http://tinyurl.com/y8zfbfh --Steve