On the size of planarly connected crossing graphs

Eyal Ackerman, Balázs Keszegh, Mate Vizer

Research output: Contribution to journalArticlepeer-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
Pages (from-to)11-22
Number of pages12
JournalJournal of Graph Algorithms and Applications
Issue number1
StatePublished - 1 Jan 2018

Bibliographical note

Funding Information:
Most of this work was done during a visit of the first author to the Rényi Institute that was partially supported by the National Research, Development and Innovation Office – NKFIH under the grant PD 108406 and by the ERC Advanced Research Grant no. 267165 (DIS-CONV). The second author was supported by the NKFIH under the grant PD 108406 and K 116769 and by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The third author was supported by the NKFIH under the grant SNN 116095. E-mail addresses: ackerman@sci.haifa.ac.il (Eyal Ackerman) keszegh.balazs@renyi.mta.hu (Balázs Keszegh) vizermate@gmail.com (Mate Vizer)

Publisher Copyright:
© 2018, Brown University. All rights reserved.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)
  • Computer Science Applications
  • Geometry and Topology
  • Computational Theory and Mathematics


Dive into the research topics of 'On the size of planarly connected crossing graphs'. Together they form a unique fingerprint.

Cite this