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
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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 -