Möbius Stanchion Systems

Consider a group of stanchions linked together in a waiting line. In order to paint both sides of every stanchion you will need to lift your paintbrush as many times as the number of faces of the corresponding plane graph. As a lazy graph theorist you want to twist the strips between stanchions in a Möbius fashion such that you do not need to lift up your paintbrush. We call such a twist a MSS and we investigate the space of all MSSs of a planar graph. Our main results are that all the MSSs are connected by a series of two elementary operations, and that the space of MSSs does not depend on the planar embedding of the graph.