Characterization of unlabeled level planar graphs

J. Joseph Fowler, Stephen G Kobourov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)

Abstract

We present the set of planar graphs that always have a simultaneous geometric embedding with a strictly monotone path on the same set of n vertices, for any of the n! possible mappings. These graphs are equivalent to the set of unlabeled level planar (ULP) graphs that are level planar over all possible labelings. Our contributions are twofold. First, we provide linear time drawing algorithms for ULP graphs. Second, we provide a complete characterization of ULP graphs by showing that any other graph must contain a subgraph homeomorphic to one of seven forbidden graphs.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages37-49
Number of pages13
Volume4875 LNCS
DOIs
StatePublished - 2008
Event15th International Symposium on Graph Drawing, GD 2007 - Sydney, Australia
Duration: Sep 24 2007Sep 26 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4875 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other15th International Symposium on Graph Drawing, GD 2007
CountryAustralia
CitySydney
Period9/24/079/26/07

Fingerprint

Drawing (graphics)
Planar graph
Labeling
Graph in graph theory
Homeomorphic
Linear Time
Subgraph
Monotone
Strictly
Path

ASJC Scopus subject areas

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

Cite this

Fowler, J. J., & Kobourov, S. G. (2008). Characterization of unlabeled level planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4875 LNCS, pp. 37-49). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4875 LNCS). https://doi.org/10.1007/978-3-540-77537-9_7

Characterization of unlabeled level planar graphs. / Fowler, J. Joseph; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4875 LNCS 2008. p. 37-49 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4875 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Fowler, JJ & Kobourov, SG 2008, Characterization of unlabeled level planar graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4875 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4875 LNCS, pp. 37-49, 15th International Symposium on Graph Drawing, GD 2007, Sydney, Australia, 9/24/07. https://doi.org/10.1007/978-3-540-77537-9_7
Fowler JJ, Kobourov SG. Characterization of unlabeled level planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4875 LNCS. 2008. p. 37-49. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-77537-9_7
Fowler, J. Joseph ; Kobourov, Stephen G. / Characterization of unlabeled level planar graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4875 LNCS 2008. pp. 37-49 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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