Graphs with large total angular resolution

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

doi:https://doi.org/10.1007/978-3-030-35802-0

Graphs with large total angular resolution

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

Institut für Softwaretechnologie (7160)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in einem Konferenzband › Begutachtung

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.

Originalsprache	englisch
Titel	Graph Drawing and Network Visualization
Herausgeber (Verlag)	Springer, Cham
Kapitel	Quality Metrics
Seiten	193-199
Seitenumfang	7
ISBN (elektronisch)	978-3-030-35802-0
ISBN (Print)	978-3-030-35801-3
DOIs	https://doi.org/10.1007/978-3-030-35802-0
Publikationsstatus	Veröffentlicht - 2019
Veranstaltung	27th International Symposium on Graph Drawing and Network Visualization: GD 2019 - Hotel Floret, Pruhonice, Tschechische Republik Dauer: 17 Sep. 2019 → 20 Sep. 2019 https://kam.mff.cuni.cz/gd2019/index.html https://kam.mff.cuni.cz/gd2019/

Publikationsreihe

Name	Lecture Notes in Computer Science
Herausgeber (Verlag)	Springer, Cham
Nummer	11904
ISSN (Print)	0302-9743
ISSN (elektronisch)	1611-3349

Konferenz

Konferenz	27th International Symposium on Graph Drawing and Network Visualization
Kurztitel	GD 2019
Land/Gebiet	Tschechische Republik
Ort	Pruhonice
Zeitraum	17/09/19 → 20/09/19
Internetadresse	https://kam.mff.cuni.cz/gd2019/index.html https://kam.mff.cuni.cz/gd2019/

Zugriff auf Dokument

https://doi.org/10.1007/978-3-030-35802-0

Dieses zitieren

Aichholzer, O, Korman, M, Okamoto, Y, De Parada, IM, Perz, D, Renssen, AV & Vogtenhuber, B 2019, Graphs with large total angular resolution. in Graph Drawing and Network Visualization. Lecture Notes in Computer Science, Nr. 11904, Springer, Cham, S. 193-199, 27th International Symposium on Graph Drawing and Network Visualization, Pruhonice, Tschechische Republik, 17/09/19. https://doi.org/10.1007/978-3-030-35802-0

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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.",

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AU - Aichholzer, Oswin

AU - Korman, Matias

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AU - De Parada, Irene Maria

AU - Perz, Daniel

AU - Renssen, André van

AU - Vogtenhuber, Birgit

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AB - 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.

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