Two Trees Which Are Self–intersecting When Drawn Simultaneously

  • Markus Geyer
  • Michael Kaufmann
  • Imrich Vrťo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

Abstract

An actual topic in the graph drawing is the question how to draw two edge sets on the same vertex set, the so-called simultaneous drawing of graphs. The goal is to simultaneously find a nice drawing for both of the sets. It has been found out that only restricted classes of planar graphs can be drawn simultaneously using straight lines and without crossings within the same edge set. In this paper, we negatively answer one of the most often posted open questions namely whether any two trees with the same vertex set can be drawn simultaneously crossing-free in a straight line way.

References

  1. 1.
    Brass, P., Cenek, E., Duncan, A., Efrat, A., Erten, C., Ismailescu, D., Kobourov, S., Lubiw, A., Mitchell, J.S.B.: On Simultaneous Planar Graph Embeddings. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 243–255. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Duncan, C.A., Eppstein, D., Kobourov, S.G.: The Geometric Thickness of Low Degree Graphs. In: Boissonant, J.-D., Snoeyink, J. (eds.) 23rd Annual Symp. on Computational geometry, pp. 340–346. ACM Press, New York (2004)Google Scholar
  3. 3.
    Erten, C., Kobourov, S.G.: Simultaneous Embedding of a Planar Graph and its Dual on the Grid. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 575–587. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Erten, C., Kobourov, S.G., Le, V., Navabi, A.: Simultaneous Graph Drawing: Layout Algorithms and Visualization Schemes. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 437–449. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Erten, C., Kobourov, S.G.: Simultaneous Embedding of Planar Graphs with Few Bends. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 195–205. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Kobourov, S.G., Pitta, C.: An Interactive Multi-User System for Simultaneous Graph Drawing. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 492–501. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Markus Geyer
    • 1
  • Michael Kaufmann
    • 1
  • Imrich Vrťo
    • 2
  1. 1.WSI für InformatikUniversität TübingenTübingenGermany
  2. 2.Institute of MathematicsSlovak Academy of SciencesBratislavaSlovakia

Personalised recommendations