Graphs with Large Total Angular Resolution

Oswin Aichholzer; Matias Korman; Yoshio Okamoto; Irene Parada; Daniel Perz; André van Renssen; Birgit Vogtenhuber

doi:10.1007/978-3-030-35802-0_15

Graphs with Large Total Angular Resolution

Oswin Aichholzer, Matias Korman, Yoshio Okamoto, Irene Parada, Daniel Perz, André van Renssen, Birgit Vogtenhuber

INF - System Information Sciences

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

Abstract

The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove that, up to a finite number of well specified exceptions of constant size, the number of edges of a graph with n vertices and a total angular resolution greater than 60 is bounded by 2n-6. This bound is tight. In addition, we show that deciding whether a graph has total angular resolution at least 60 is NP-hard.

Original language	English
Title of host publication	Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings
Editors	Daniel Archambault, Csaba D. Tóth
Publisher	Springer
Pages	193-199
Number of pages	7
ISBN (Print)	9783030358013
DOIs	https://doi.org/10.1007/978-3-030-35802-0_15
Publication status	Published - 2019
Event	27th International Symposium on Graph Drawing and Network Visualization, GD 2019 - Prague, Czech Republic Duration: 2019 Sep 17 → 2019 Sep 20

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11904 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Symposium on Graph Drawing and Network Visualization, GD 2019
Country	Czech Republic
City	Prague
Period	19/9/17 → 19/9/20

Keywords

Angular resolution
Crossing resolution
Graph drawing
NP-hardness
Total angular resolution

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-35802-0_15

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Aichholzer, O., Korman, M., Okamoto, Y., Parada, I., Perz, D., van Renssen, A., & Vogtenhuber, B. (2019). Graphs with Large Total Angular Resolution. In D. Archambault, & C. D. Tóth (Eds.), Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings (pp. 193-199). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11904 LNCS). Springer. https://doi.org/10.1007/978-3-030-35802-0_15

Graphs with Large Total Angular Resolution. / Aichholzer, Oswin; Korman, Matias; Okamoto, Yoshio; Parada, Irene; Perz, Daniel; van Renssen, André; Vogtenhuber, Birgit.

Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. ed. / Daniel Archambault; Csaba D. Tóth. Springer, 2019. p. 193-199 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11904 LNCS).

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

Aichholzer, O, Korman, M, Okamoto, Y, Parada, I, Perz, D, van Renssen, A & Vogtenhuber, B 2019, Graphs with Large Total Angular Resolution. in D Archambault & CD Tóth (eds), Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11904 LNCS, Springer, pp. 193-199, 27th International Symposium on Graph Drawing and Network Visualization, GD 2019, Prague, Czech Republic, 19/9/17. https://doi.org/10.1007/978-3-030-35802-0_15

Aichholzer O, Korman M, Okamoto Y, Parada I, Perz D, van Renssen A et al. Graphs with Large Total Angular Resolution. In Archambault D, Tóth CD, editors, Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. Springer. 2019. p. 193-199. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-35802-0_15

Aichholzer, Oswin ; Korman, Matias ; Okamoto, Yoshio ; Parada, Irene ; Perz, Daniel ; van Renssen, André ; Vogtenhuber, Birgit. / Graphs with Large Total Angular Resolution. Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. editor / Daniel Archambault ; Csaba D. Tóth. Springer, 2019. pp. 193-199 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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