Discrete & Computational Geometry

, Volume 43, Issue 2, pp 272–288

Universal Sets of n Points for One-bend Drawings of Planar Graphs with n Vertices

  • Hazel Everett
  • Sylvain Lazard
  • Giuseppe Liotta
  • Stephen Wismath
Article

DOI: 10.1007/s00454-009-9149-3

Cite this article as:
Everett, H., Lazard, S., Liotta, G. et al. Discrete Comput Geom (2010) 43: 272. doi:10.1007/s00454-009-9149-3

Abstract

This paper shows that any planar graph with n vertices can be point-set embedded with at most one bend per edge on a universal set of n points in the plane. An implication of this result is that any number of planar graphs admit a simultaneous embedding without mapping with at most one bend per edge.

Keywords

Graph drawingUniversal point setsOne-bend drawingsSimultaneous embeddings

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Hazel Everett
    • 1
  • Sylvain Lazard
    • 1
  • Giuseppe Liotta
    • 2
  • Stephen Wismath
    • 3
  1. 1.INRIA Nancy Grand EstUniversité Nancy 2, LORIANancyFrance
  2. 2.Dip. di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di PerugiaPerugiaItaly
  3. 3.Department of Mathematics and Computer ScienceUniversity of LethbridgeLethbridgeCanada