Graphs with large total angular resolution

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

doi:10.1016/j.tcs.2022.12.010

Graphs with large total angular resolution

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

^*Corresponding author for this work

Institute of Software Technology (7160)

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

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 tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least 60^∘ is NP-hard. Further we present some special graphs and their total angular resolution.

Original language	English
Pages (from-to)	73-88
Number of pages	16
Journal	Theoretical Computer Science
Volume	943
DOIs	https://doi.org/10.1016/j.tcs.2022.12.010
Publication status	Published - 17 Jan 2023

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1016/j.tcs.2022.12.010Licence: CC BY 4.0

Cite this

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title = "Graphs with large total angular resolution",

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 tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least 60∘ is NP-hard. Further we present some special graphs and their total angular resolution.",

keywords = "Angular resolution, Crossing resolution, Graph drawing, NP-hardness, Total angular resolution",

author = "Oswin Aichholzer and Matias Korman and Yoshio Okamoto and Irene Parada and Daniel Perz and {van Renssen}, Andr{\'e} and Birgit Vogtenhuber",

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doi = "10.1016/j.tcs.2022.12.010",

language = "English",

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T1 - Graphs with large total angular resolution

AU - Aichholzer, Oswin

AU - Korman, Matias

AU - Okamoto, Yoshio

AU - Parada, Irene

AU - Perz, Daniel

AU - van Renssen, André

AU - Vogtenhuber, Birgit

PY - 2023/1/17

Y1 - 2023/1/17

N2 - 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 tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least 60∘ is NP-hard. Further we present some special graphs and their total angular resolution.

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 tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least 60∘ is NP-hard. Further we present some special graphs and their total angular resolution.

KW - Angular resolution

KW - Crossing resolution

KW - Graph drawing

KW - NP-hardness

KW - Total angular resolution

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DO - 10.1016/j.tcs.2022.12.010

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VL - 943

SP - 73

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JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

Graphs with large total angular resolution

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

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