Constrained simultaneous and near-simultaneous embeddings

Fabrizio Frati, Michael Kaufmann, Stephen G Kobourov

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A geometric simultaneous embedding of two graphs G 1=(V 1,E 1) and G 2=(V 2,E 2) with a bijective mapping of their vertex sets γ:V 1 → V 2 is a pair of planar straight-line drawings Γ 1 of G 1 and Γ 2 of G 2, such that each vertex v2=γ(v1), with v1 ∈ V 1 and v2 ∈ V 2, is mapped in Γ 2 to the same point where v1 is mapped in Γ 1. In this paper we examine several constrained versions and a relaxed version of the geometric simultaneous embedding problem. We show that assuming that the input graphs do not share common edges does not yield larger classes of graphs that can be simultaneously embedded. Further, if a prescribed combinatorial embedding for each input graph must be preserved, then we can answer some of the problems that are still open in the standard geometric simultaneous embedding setting. Finally, we present some results on the near-simultaneous embedding problem, in which vertices are not forced to be placed exactly at the same, but just at 'nearby' points in different drawings.

Original languageEnglish (US)
Pages (from-to)447-465
Number of pages19
JournalJournal of Graph Algorithms and Applications
Volume13
Issue number3
DOIs
StatePublished - 2009

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Drawing (graphics)
Embedding Problem
Graph in graph theory
Line Drawing
Bijective
Vertex of a graph
Straight Line

ASJC Scopus subject areas

  • Geometry and Topology
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Science(all)
  • Computer Science Applications

Cite this

Constrained simultaneous and near-simultaneous embeddings. / Frati, Fabrizio; Kaufmann, Michael; Kobourov, Stephen G.

In: Journal of Graph Algorithms and Applications, Vol. 13, No. 3, 2009, p. 447-465.

Research output: Contribution to journalArticle

Frati, Fabrizio ; Kaufmann, Michael ; Kobourov, Stephen G. / Constrained simultaneous and near-simultaneous embeddings. In: Journal of Graph Algorithms and Applications. 2009 ; Vol. 13, No. 3. pp. 447-465.
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