On the size of graphs that admit polyline drawings with few bends and crossing angles

Eyal Ackerman; Radoslav Fulek; Csaba D. Tóth

doi:10.1007/978-3-642-18469-7_1

On the size of graphs that admit polyline drawings with few bends and crossing angles

Eyal Ackerman, Radoslav Fulek, Csaba D. Tóth

Faculty of Natural Sciences

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

Abstract

We consider graphs that admit polyline drawings where all crossings occur at the same angle α ∈ (0, π/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
Title of host publication	Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers
Pages	1-12
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-18469-7_1
State	Published - 2011
Event	18th International Symposium on Graph Drawing, GD 2010 - Konstanz, Germany Duration: 21 Sep 2010 → 24 Sep 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6502 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th International Symposium on Graph Drawing, GD 2010
Country/Territory	Germany
City	Konstanz
Period	21/09/10 → 24/09/10

Bibliographical note

Funding Information:
★ Partially supported by NSERC grant RGPIN 35586.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-18469-7_1

Cite this

Ackerman, E., Fulek, R., & Tóth, C. D. (2011). On the size of graphs that admit polyline drawings with few bends and crossing angles. In Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers (pp. 1-12). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6502 LNCS). https://doi.org/10.1007/978-3-642-18469-7_1

Ackerman, Eyal ; Fulek, Radoslav ; Tóth, Csaba D. / On the size of graphs that admit polyline drawings with few bends and crossing angles. Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers. 2011. pp. 1-12 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We consider graphs that admit polyline drawings where all crossings occur at the same angle α ∈ (0, π/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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note = "Funding Information: ★ Partially supported by NSERC grant RGPIN 35586.; 18th International Symposium on Graph Drawing, GD 2010 ; Conference date: 21-09-2010 Through 24-09-2010",

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Ackerman, E, Fulek, R & Tóth, CD 2011, On the size of graphs that admit polyline drawings with few bends and crossing angles. in Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6502 LNCS, pp. 1-12, 18th International Symposium on Graph Drawing, GD 2010, Konstanz, Germany, 21/09/10. https://doi.org/10.1007/978-3-642-18469-7_1

On the size of graphs that admit polyline drawings with few bends and crossing angles. / Ackerman, Eyal; Fulek, Radoslav; Tóth, Csaba D.
Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers. 2011. p. 1-12 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6502 LNCS).

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

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Ackerman E, Fulek R, Tóth CD. On the size of graphs that admit polyline drawings with few bends and crossing angles. In Graph Drawing - 18th International Symposium, GD 2010, Revised Selected Papers. 2011. p. 1-12. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-18469-7_1

On the size of graphs that admit polyline drawings with few bends and crossing angles

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