On simultaneous planar graph embeddings

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

Research output: Chapter in Book/Report/Conference proceedingChapter

19 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. 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(n2) x O(n2) grid.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsFrank Dehne, Jorg-Rudiger Sack, Michiel Smid
PublisherSpringer-Verlag
Pages243-255
Number of pages13
ISBN (Print)3540405453
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2748
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Brass, P., Cenek, E., Duncan, C. A., Efrat, A., Erten, C., Ismailescu, D., Kobourov, S. G., Lubiw, A., & Mitchell, J. S. B. (2003). On simultaneous planar graph embeddings. In F. Dehne, J-R. Sack, & M. Smid (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 243-255). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2748). Springer-Verlag. https://doi.org/10.1007/978-3-540-45078-8_22