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Graphs with Large Total Angular Resolution

  • Oswin Aichholzer
  • Matias Korman
  • Yoshio Okamoto
  • Irene Parada
  • Daniel PerzEmail author
  • André van Renssen
  • Birgit Vogtenhuber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

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 \(60^{\circ }\) is bounded by \(2n-6\). This bound is tight. In addition, we show that deciding whether a graph has total angular resolution at least \(60^{\circ }\) is NP-hard.

Keywords

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

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graz University of TechnologyGrazAustria
  2. 2.Tufts UniversityMedfordUSA
  3. 3.The University of Electro-Communications and RIKEN Center for Advanced Intelligence ProjectTokyoJapan
  4. 4.The University of SydneySydneyAustralia

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