On the size of planarly connected crossing graphs

Eyal Ackerman; Balázs Keszegh; Mate Vizer

doi:10.7155/jgaa.00453

On the size of planarly connected crossing graphs

Eyal Ackerman, Balázs Keszegh, Mate Vizer

Faculty of Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	11-22
Number of pages	12
Journal	Journal of Graph Algorithms and Applications
Volume	22
Issue number	1
DOIs	https://doi.org/10.7155/jgaa.00453
State	Published - 1 Jan 2018

Bibliographical note

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

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Science Applications
Geometry and Topology
Computational Theory and Mathematics

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10.7155/jgaa.00453

Cite this

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AB - 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.

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On the size of planarly connected crossing graphs

Abstract

Bibliographical note

ASJC Scopus subject areas

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