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The Planar Slope Number of Subcubic Graphs

  • Emilio Di Giacomo
  • Giuseppe Liotta
  • Fabrizio Montecchiani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

A subcubic planar graph is a planar graph whose vertices have degree at most three. We show that the subcubic planar graphs with at least five vertices have planar slope number at most four, which is worst case optimal. This answers an open question by Jelínek et al. [6]. As a corollary, we prove that the subcubic planar graphs with at least five vertices have angular resolution π/4, which solves an open problem by Kant [7] and by Formann et al. [4].

Keywords

Planar Graph Outerplanar Graph Split Component Virtual Edge Basic Slope 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Giuseppe Liotta
    • 1
  • Fabrizio Montecchiani
    • 1
  1. 1.Dip. di IngegneriaUniversità degli Studi di PerugiaItaly

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