Planar Octilinear Drawings with One Bend Per Edge

  • Michael A. Bekos
  • Martin Gronemann
  • Michael Kaufmann
  • Robert Krug
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A k-planar graph is a planar graph in which each vertex has degree less or equal to k. In particular, we prove that every 4-planar graph admits a planar octilinear drawing with at most one bend per edge on an integer grid of size O(n2) ×O(n). For 5-planar graphs, we prove that one bend per edge still suffices in order to construct planar octilinear drawings, but in super-polynomial area. However, for 6-planar graphs we give a class of graphs whose planar octilinear drawings require at least two bends per edge.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Martin Gronemann
    • 2
  • Michael Kaufmann
    • 1
  • Robert Krug
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  2. 2.Institut für InformatikUniversität zu KölnGermany

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