Simultaneous Embedding of a Planar Graph and Its Dual on the Grid

Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should cross only their corresponding primal edges. We consider the problem of simultaneously embedding a planar graph and its dual on a small integer grid such that the edges are drawn as straight-line segments and the only crossings are between primal-dual pairs of edges. We provide an O(n) time algorithm that simultaneously embeds a 3-connected planar graph and its dual on a (2n - 2)

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Cesim Erten, Stephen G. Kobourov
• Keywords: CORR 2002, Corresponding Primal Edges, Corresponding Primal Faces, Education, Planar Graph