On the maximum number of edges in topological graphs with no four pairwise crossing edges

Eyal Ackerman

doi:10.1007/s00454-009-9143-9

On the maximum number of edges in topological graphs with no four pairwise crossing edges

Eyal Ackerman

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

Abstract

A topological graph is called k -quasi-planar if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k=4.

Original language	English
Pages (from-to)	365-375
Number of pages	11
Journal	Discrete and Computational Geometry
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s00454-009-9143-9
State	Published - Apr 2009
Externally published	Yes

Keywords

Discharging method
Geometric graphs
Quasi-planar graphs
Topological graphs

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-009-9143-9

Cite this

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abstract = "A topological graph is called k -quasi-planar if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k=4.",

keywords = "Discharging method, Geometric graphs, Quasi-planar graphs, Topological graphs",

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AB - A topological graph is called k -quasi-planar if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k=4.

KW - Discharging method

KW - Geometric graphs

KW - Quasi-planar graphs

KW - Topological graphs

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M3 - Article

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JO - Discrete and Computational Geometry

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ER -

On the maximum number of edges in topological graphs with no four pairwise crossing edges

Abstract

Keywords

ASJC Scopus subject areas

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