Simultaneous embedding of a planar graph and its dual on the grid

Cesim Erten, Stephen G. Kobourov

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

Traditional representations of graphs and their duals suggest that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should only cross 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) × (2n - 2) integer grid, where n is the total number of vertices in the graph and its dual. All the edges are drawn as straight-line segments except for one edge on the outer face, which is drawn using two segments.

Original languageEnglish (US)
Pages (from-to)313-327
Number of pages15
JournalTheory of Computing Systems
Volume38
Issue number3
DOIs
StatePublished - May 1 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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