Graphs with large total angular resolution

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-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 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.
Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization
PublisherSpringer, Cham
ChapterQuality Metrics
Pages193-199
Number of pages7
ISBN (Electronic)978-3-030-35802-0
ISBN (Print)978-3-030-35801-3
DOIs
Publication statusPublished - 2019
Event27th International Symposium on Graph Drawing and Network Visualization - Hotel Floret, Pruhonice, Czech Republic
Duration: 17 Sep 201920 Sep 2019
https://kam.mff.cuni.cz/gd2019/index.html
https://kam.mff.cuni.cz/gd2019/

Publication series

NameLecture Notes in Computer Science
PublisherSpringer, Cham
Number11904
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference27th International Symposium on Graph Drawing and Network Visualization
Abbreviated titleGD 2019
CountryCzech Republic
CityPruhonice
Period17/09/1920/09/19
Internet address

Cite this

Aichholzer, O., Korman, M., Okamoto, Y., De Parada, I. M., Perz, D., Renssen, A. V., & Vogtenhuber, B. (2019). Graphs with large total angular resolution. In Graph Drawing and Network Visualization (pp. 193-199). (Lecture Notes in Computer Science; No. 11904). Springer, Cham. https://doi.org/10.1007/978-3-030-35802-0