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Drawing Planar Graphs with Few Segments on a Polynomial Grid

  • Philipp KindermannEmail author
  • Tamara Mchedlidze
  • Thomas Schneck
  • Antonios Symvonis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

Abstract

The visual complexity of a graph drawing can be measured by the number of geometric objects used for the representation of its elements. In this paper, we study planar graph drawings where edges are represented by few segments. In such a drawing, one segment may represent multiple edges forming a path. Drawings of planar graphs with few segments were intensively studied in the past years. However, the area requirements were only considered for limited subclasses of planar graphs. In this paper, we show that trees have drawings with \(3n/4-1\) segments and \(n^2\) area, improving the previous result of \(O(n^{3.58})\). We also show that 3-connected planar graphs and biconnected outerplanar graphs have a drawing with \(8n/3-O(1)\) and \(3n/2-O(1)\) segments, respectively, and \(O(n^3)\) area.

Notes

Acknowledgements

We thank Roman Prutkin for the initial discussion of the problem and Therese Biedl for helpful comments.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universität WürzburgWürzburgGermany
  2. 2.Karlsruhe Institute of Technology (KIT)KarlsruheGermany
  3. 3.Universitä TübingenTübingenGermany
  4. 4.National Technical University of AthensAthensGreece

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