Graphs that admit polyline drawings with few crossing angles

Eyal Ackerman; Radoslav Fulek; Csaba D. Tóth

doi:10.1137/100819564

Graphs that admit polyline drawings with few crossing angles

Eyal Ackerman
, Radoslav Fulek
, Csaba D. Tóth

Faculty of Natural Sciences

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

Abstract

We consider graphs that admit polyline drawings where all crossings occur at the same angle a ε (0, φ 2 ]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This result remains true when each crossing occurs at an angle from a small set of angles. We also provide several extensions that might be of independent interest.

Original language	English
Pages (from-to)	305-320
Number of pages	16
Journal	SIAM Journal on Discrete Mathematics
Volume	26
Issue number	1
DOIs	https://doi.org/10.1137/100819564
State	Published - 2012

Keywords

Crossing number
Geometric graph
Polyline drawing

ASJC Scopus subject areas

General Mathematics

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10.1137/100819564

Cite this

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title = "Graphs that admit polyline drawings with few crossing angles",

abstract = "We consider graphs that admit polyline drawings where all crossings occur at the same angle a ε (0, φ 2 ]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This result remains true when each crossing occurs at an angle from a small set of angles. We also provide several extensions that might be of independent interest.",

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AU - Ackerman, Eyal

AU - Fulek, Radoslav

AU - Tóth, Csaba D.

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AB - We consider graphs that admit polyline drawings where all crossings occur at the same angle a ε (0, φ 2 ]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This result remains true when each crossing occurs at an angle from a small set of angles. We also provide several extensions that might be of independent interest.

KW - Crossing number

KW - Geometric graph

KW - Polyline drawing

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DO - 10.1137/100819564

M3 - Article

AN - SCOPUS:84861595475

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JO - SIAM Journal on Discrete Mathematics

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Graphs that admit polyline drawings with few crossing angles

Abstract

Keywords

ASJC Scopus subject areas

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