@inproceedings{0338ac7c072f47b592cc1ba9628e45a9,
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 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.",
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",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-35802-0_15",
language = "English",
isbn = "9783030358013",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer",
pages = "193--199",
editor = "Daniel Archambault and T{\'o}th, {Csaba D.}",
booktitle = "Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings",
note = "27th International Symposium on Graph Drawing and Network Visualization, GD 2019 ; Conference date: 17-09-2019 Through 20-09-2019",
}