On the size of planarly connected crossing graphs

Eyal Ackerman, Balázs Keszegh, Mate Vizer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We prove that if an n-vertex graph G can be drawn in the plane such that each pair of crossing edges is independent and there is a crossing-free edge that connects their endpoints, then G has O(n) edges. Graphs that admit such drawings are related to quasi-planar graphs and to maximal 1-planar and fan-planar graphs.

Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers
EditorsMartin Nollenburg, Yifan Hu
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783319501055
StatePublished - 2016
Event24th International Symposium on Graph Drawing and Network Visualization, GD 2016 - Athens, Greece
Duration: 19 Sep 201621 Sep 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9801 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Symposium on Graph Drawing and Network Visualization, GD 2016

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2016.


  • 1-planar graphs
  • Crossing edges
  • Crossing-free edge
  • Fanplanar graphs
  • Planar graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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