On simultaneous planar graph embeddings

Peter Brass, Eowyn Cenek, Cristian A. Duncan, Alon Efrat, Cesim Erten, Dan P. Ismailescu, Stephen G. Kobourov, Anna Lubiw, Joseph S.B. Mitchell

Research output: Contribution to journalArticlepeer-review

98 Scopus citations

Abstract

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. We present positive and negative results for the two versions of the problem. Among the positive results with given mapping, we show that we can embed two paths on an n×n grid, and two caterpillar graphs on a 3n×3n grid. Among the negative results with given mapping, we show that it is not always possible to simultaneously embed three paths or two general planar graphs. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n2)×O( n2) grid.

Original languageEnglish (US)
Pages (from-to)117-130
Number of pages14
JournalComputational Geometry: Theory and Applications
Volume36
Issue number2
DOIs
StatePublished - Feb 1 2007

Keywords

  • Graph drawing
  • Planar graphs
  • Simultaneous visualizations

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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