Monotone Simultaneous Embeddings of Paths in d Dimensions

  • David Bremner
  • Olivier Devillers
  • Marc Glisse
  • Sylvain Lazard
  • Giuseppe Liotta
  • Tamara Mchedlidze
  • Sue Whitesides
  • Stephen Wismath
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

Abstract

We study the following problem: Given k paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that, for any dimension d, there is a set of \(d+1\) paths that does not admit a monotone simultaneous geometric embedding.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • David Bremner
    • 1
  • Olivier Devillers
    • 2
  • Marc Glisse
    • 3
  • Sylvain Lazard
    • 2
  • Giuseppe Liotta
    • 4
  • Tamara Mchedlidze
    • 5
  • Sue Whitesides
    • 6
  • Stephen Wismath
    • 7
  1. 1.University of New BrunswickFrederictonCanada
  2. 2.Inria, CNRS, University of LorraineNancyFrance
  3. 3.InriaSaclayFrance
  4. 4.University of PerugiaPerugiaItaly
  5. 5.Karlsruhe Institute of TechnologyKarlsruheGermany
  6. 6.University of VictoriaVictoriaCanada
  7. 7.University of LethbridgeLethbridgeCanada

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