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

38 Scopus citations

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 publicationGraph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers
Pages83-94
Number of pages12
DOIs
StatePublished - Dec 1 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

Other

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Straight-line grid drawings of 3-connected 1-planar graphs'. Together they form a unique fingerprint.

  • Cite this

    Alam, M. J., Brandenburg, F. J., & Kobourov, S. G. (2013). Straight-line grid drawings of 3-connected 1-planar graphs. In Graph Drawing - 21st International Symposium, GD 2013, Revised Selected Papers (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