Straight-line grid drawings of 3-connected 1-planar graphs

Md Jawaherul Alam, Franz J. Brandenburg, Stephen G Kobourov

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

35 Citations (Scopus)

Abstract

A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages83-94
Number of pages12
Volume8242 LNCS
DOIs
StatePublished - 2013
Event21st International Symposium on Graph Drawing, GD 2013 - Bordeaux, France
Duration: Sep 23 2013Sep 25 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8242 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other21st International Symposium on Graph Drawing, GD 2013
CountryFrance
CityBordeaux
Period9/23/139/25/13

Fingerprint

Line Drawing
Straight Line
Planar graph
Grid
Graph in graph theory
Exception
Linear Time
Face
Integer
Drawing

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Alam, M. J., Brandenburg, F. J., & Kobourov, S. G. (2013). Straight-line grid drawings of 3-connected 1-planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8242 LNCS, pp. 83-94). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8242 LNCS). https://doi.org/10.1007/978-3-319-03841-4-8

Straight-line grid drawings of 3-connected 1-planar graphs. / Alam, Md Jawaherul; Brandenburg, Franz J.; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8242 LNCS 2013. p. 83-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8242 LNCS).

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

Alam, MJ, Brandenburg, FJ & Kobourov, SG 2013, Straight-line grid drawings of 3-connected 1-planar graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 8242 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8242 LNCS, pp. 83-94, 21st International Symposium on Graph Drawing, GD 2013, Bordeaux, France, 9/23/13. https://doi.org/10.1007/978-3-319-03841-4-8
Alam MJ, Brandenburg FJ, Kobourov SG. Straight-line grid drawings of 3-connected 1-planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8242 LNCS. 2013. p. 83-94. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-03841-4-8
Alam, Md Jawaherul ; Brandenburg, Franz J. ; Kobourov, Stephen G. / Straight-line grid drawings of 3-connected 1-planar graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8242 LNCS 2013. pp. 83-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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