On the size of planarly connected crossing graphs

Eyal Ackerman; Balázs Keszegh; Mate Vizer

doi:10.1007/978-3-319-50106-2_24

On the size of planarly connected crossing graphs

Eyal Ackerman, Balázs Keszegh, Mate Vizer

Faculty of Natural Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › 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
Title of host publication	Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers
Editors	Martin Nollenburg, Yifan Hu
Publisher	Springer Verlag
Pages	311-320
Number of pages	10
ISBN (Print)	9783319501055
DOIs	https://doi.org/10.1007/978-3-319-50106-2_24
State	Published - 2016
Event	24th International Symposium on Graph Drawing and Network Visualization, GD 2016 - Athens, Greece Duration: 19 Sep 2016 → 21 Sep 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9801 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	24th International Symposium on Graph Drawing and Network Visualization, GD 2016
Country/Territory	Greece
City	Athens
Period	19/09/16 → 21/09/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2016.

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-50106-2_24

Cite this

Ackerman, E., Keszegh, B., & Vizer, M. (2016). On the size of planarly connected crossing graphs. In M. Nollenburg, & Y. Hu (Eds.), Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers (pp. 311-320). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9801 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-50106-2_24

Ackerman, Eyal ; Keszegh, Balázs ; Vizer, Mate. / On the size of planarly connected crossing graphs. Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers. editor / Martin Nollenburg ; Yifan Hu. Springer Verlag, 2016. pp. 311-320 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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author = "Eyal Ackerman and Bal{\'a}zs Keszegh and Mate Vizer",

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Ackerman, E, Keszegh, B & Vizer, M 2016, On the size of planarly connected crossing graphs. in M Nollenburg & Y Hu (eds), Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9801 LNCS, Springer Verlag, pp. 311-320, 24th International Symposium on Graph Drawing and Network Visualization, GD 2016, Athens, Greece, 19/09/16. https://doi.org/10.1007/978-3-319-50106-2_24

On the size of planarly connected crossing graphs. / Ackerman, Eyal; Keszegh, Balázs; Vizer, Mate.
Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers. ed. / Martin Nollenburg; Yifan Hu. Springer Verlag, 2016. p. 311-320 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9801 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ackerman E, Keszegh B, Vizer M. On the size of planarly connected crossing graphs. In Nollenburg M, Hu Y, editors, Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers. Springer Verlag. 2016. p. 311-320. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-50106-2_24

On the size of planarly connected crossing graphs

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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