TY - GEN

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

N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019

Y1 - 2019

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 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.

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.

KW - Angular resolution

KW - Crossing resolution

KW - Graph drawing

KW - NP-hardness

KW - Total angular resolution

UR - http://www.scopus.com/inward/record.url?scp=85076913209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076913209&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-35802-0_15

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

M3 - Conference contribution

AN - SCOPUS:85076913209

SN - 9783030358013

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 193

EP - 199

BT - Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings

A2 - Archambault, Daniel

A2 - Tóth, Csaba D.

PB - Springer

T2 - 27th International Symposium on Graph Drawing and Network Visualization, GD 2019

Y2 - 17 September 2019 through 20 September 2019

ER -