Planarity testing for graphs represented by a rotation scheme

Many algorithms exist to determine if a given graph can be embedded in a plane [G. Di Battistia et al., (1994)]. The majority of these methods, however, are only valid for simple graphs and do not take into account the order of edges emanating from each vertex. There are many areas, such as communication design, genetics, group theory, network optimisation and VLSI, where the ordering of edges is crucial to the representation of a system. Rotation schemes can be used to store the ordering of edges around a vertex. Let G be an arbitrary, possibly nonsimple, graph. We provide an algorithm that determines, from the rotation scheme of G, if G can be embedded in the plane. If the rotation scheme of G can be realised by a planar drawing, the regions of G are returned.