Graphs with Large Total Angular Resolution

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 - 27th International Symposium, GD 2019, Proceedings
EditorsDaniel Archambault, Csaba D. Tóth
PublisherSpringer
Pages193-199
Number of pages7
ISBN (Print)9783030358013
DOIs
Publication statusPublished - 2019 Jan 1
Externally publishedYes
Event27th International Symposium on Graph Drawing and Network Visualization, GD 2019 - Prague, Czech Republic
Duration: 2019 Sep 172019 Sep 20

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11904 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference27th International Symposium on Graph Drawing and Network Visualization, GD 2019
CountryCzech Republic
CityPrague
Period19/9/1719/9/20

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Graphs with Large Total Angular Resolution'. Together they form a unique fingerprint.

  • Cite this

    Aichholzer, O., Korman, M., Okamoto, Y., Parada, I., Perz, D., van Renssen, A., & Vogtenhuber, B. (2019). Graphs with Large Total Angular Resolution. In D. Archambault, & C. D. Tóth (Eds.), Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings (pp. 193-199). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11904 LNCS). Springer. https://doi.org/10.1007/978-3-030-35802-0_15