Minimum Level Nonplanar Patterns for Trees

  • J. Joseph Fowler
  • Stephen G. Kobourov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)

Abstract

minimum Level Nonplanar (MLNP) patterns play the role for level planar graphs that the forbidden Kuratowksi subdivisions K 5 and K 3,3 play for planar graphs. We add two (MLNP) patterns for trees to the previous set of tree patterns given by Healy et al. [4]. Neither of these patterns match any of the previous patterns. We show that this new set of patterns completely characterizes level planar trees.

References

  1. 1.
    Di Battista, G., Nardelli, E.: Hierarchies and planarity theory. IEEE Trans. Systems Man Cybernet 18(6), 1035–1046 (1988)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Estrella-Balderrama, A., Fowler, J.J., Kobourov, S.G.: Characterization of unlabeled level planar trees. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 367–369. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Fowler, J.J., Kobourov, S.G.: Minimum level nonplanar patterns for trees. Technical Report TR07-04, University of Arizona (2007), ftp://ftp.cs.arizona.edu/reports/2007/TR07-04.pdf
  4. 4.
    Healy, P., Kuusik, A., Leipert, S.: A characterization of level planar graphs. Discrete Math. 280(1-3), 51–63 (2004)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kuratowski, C.: Sur les problèmes des courbes gauches en Topologie. Fundamenta Mathematicae 15, 271–283 (1930)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • J. Joseph Fowler
    • 1
  • Stephen G. Kobourov
    • 1
  1. 1.Department of Computer ScienceUniversity of Arizona 

Personalised recommendations