Simultaneous graph embedding with bends and circular arcs

Justin Cappos, Alejandro Estrella-Balderrama, J. Joseph Fowler, Stephen G Kobourov

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A simultaneous embedding of two vertex-labeled planar graphs on n vertices is possible if there exists a labeled point set of size n such that each of the graphs can be realized on that point set without crossings. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embedding algorithms run in O(n) time.

Original languageEnglish (US)
Pages (from-to)173-182
Number of pages10
JournalComputational Geometry: Theory and Applications
Volume42
Issue number2
DOIs
StatePublished - Feb 2009

Fingerprint

Graph Embedding
Stars
Arc of a curve
Outerplanar Graph
Path
Planar graph
Point Sets
Set of points
Star
Graph in graph theory
Vertex of a graph
Demonstrate

Keywords

  • Simultaneous embedding

ASJC Scopus subject areas

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

Cite this

Simultaneous graph embedding with bends and circular arcs. / Cappos, Justin; Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Kobourov, Stephen G.

In: Computational Geometry: Theory and Applications, Vol. 42, No. 2, 02.2009, p. 173-182.

Research output: Contribution to journalArticle

Cappos, Justin ; Estrella-Balderrama, Alejandro ; Fowler, J. Joseph ; Kobourov, Stephen G. / Simultaneous graph embedding with bends and circular arcs. In: Computational Geometry: Theory and Applications. 2009 ; Vol. 42, No. 2. pp. 173-182.
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