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Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and Large Angles

  • Philipp KindermannEmail author
  • Fabrizio Montecchiani
  • Lena Schlipf
  • André Schulz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

We show that the 1-planar slope number of 3-connected cubic 1-planar graphs is at most 4 when edges are drawn as polygonal curves with at most 1 bend each. This bound is obtained by drawings whose vertex and crossing resolution is at least \(\pi /4\). On the other hand, if the embedding is fixed, then there is a 3-connected cubic 1-planar graph that needs 3 slopes when drawn with at most 1 bend per edge. We also show that 2 slopes always suffice for 1-planar drawings of subcubic 1-planar graphs with at most 2 bends per edge. This bound is obtained with vertex resolution \(\pi /2\) and the drawing is RAC (crossing resolution \(\pi /2\)). Finally, we prove lower bounds for the slope number of straight-line 1-planar drawings in terms of number of vertices and maximum degree.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of WaterlooWaterlooCanada
  2. 2.Università degli Studi di PerugiaPerugiaItaly
  3. 3.FernUniversität in HagenHagenGermany

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