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

46 Scopus citations


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 publicationGraph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers
Number of pages12
ISBN (Print)9783319038407
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)0302-9743
ISSN (Electronic)1611-3349


Other21st International Symposium on Graph Drawing, GD 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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