July 16, 2003 to July 18, 2003
A. Donafee , University of Luton
Many algorithms exist to determine if a given graph can be embedded in a plane . 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 this 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 non-simple, 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.
A. Donafee, "Planarity Testing for Graphs Represented by A Rotation Scheme", IV, 2003, 2013 17th International Conference on Information Visualisation, 2013 17th International Conference on Information Visualisation 2003, pp. 491, doi:10.1109/IV.2003.1218030