On simultaneous planar graph embeddings

P. Brass, E. Cenek, Christian A. Duncan, Alon Efrat, C. Erten, D. Ismailescu, Stephen G Kobourov, A. Lubiw, J. S B Mitchell

Research output: Contribution to journalArticle

19 Citations (Scopus)

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. In particular, given a mapping, we show how to embed two paths on an n x n grid, and two caterpillar graphs on a 3n x 3n grid. We show that it is not always possible to simultaneously embed three paths. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n) x O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n 2) x O(n 2) grid.

Original languageEnglish (US)
Pages (from-to)243-255
Number of pages13
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2748
StatePublished - 2003

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Graph Embedding
Planar graph
Grid
Caterpillar
Outerplanar Graph
Path
Graph in graph theory

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

On simultaneous planar graph embeddings. / Brass, P.; Cenek, E.; Duncan, Christian A.; Efrat, Alon; Erten, C.; Ismailescu, D.; Kobourov, Stephen G; Lubiw, A.; Mitchell, J. S B.

In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 2748, 2003, p. 243-255.

Research output: Contribution to journalArticle

Brass, P. ; Cenek, E. ; Duncan, Christian A. ; Efrat, Alon ; Erten, C. ; Ismailescu, D. ; Kobourov, Stephen G ; Lubiw, A. ; Mitchell, J. S B. / On simultaneous planar graph embeddings. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2003 ; Vol. 2748. pp. 243-255.
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