Characterizing Simultaneous Embedding with Fixed Edges

J. J. Fowler, M. Jünger, Stephen G Kobourov, M. Schulz

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V of n vertices in the plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same Jordan curve in the simultaneous drawing. We give a necessary condition for when pairs of graphs can have a simultaneous embedding with fixed edges (SEFE). This allows us to determine for which (outer)planar graphs always have a SEFE with all (outer)planar graphs with O (n2 lg n) time drawing algorithms. This allows us to decide in O (n) time whether a pair of biconnected outerplanar graphs has a SEFE.

Original languageEnglish (US)
Pages (from-to)41-44
Number of pages4
JournalElectronic Notes in Discrete Mathematics
Volume31
Issue numberC
DOIs
StatePublished - Aug 20 2008

Fingerprint

Planar graph
Graph in graph theory
Outerplanar Graph
Jordan Curve
Necessary Conditions
Vertex of a graph
Drawing

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Characterizing Simultaneous Embedding with Fixed Edges. / Fowler, J. J.; Jünger, M.; Kobourov, Stephen G; Schulz, M.

In: Electronic Notes in Discrete Mathematics, Vol. 31, No. C, 20.08.2008, p. 41-44.

Research output: Contribution to journalArticle

Fowler, J. J. ; Jünger, M. ; Kobourov, Stephen G ; Schulz, M. / Characterizing Simultaneous Embedding with Fixed Edges. In: Electronic Notes in Discrete Mathematics. 2008 ; Vol. 31, No. C. pp. 41-44.
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