Characterization of Unlabeled Level Planar Trees

  • Alejandro Estrella-Balderrama
  • J. Joseph Fowler
  • Stephen G. Kobourov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)


Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓ j  = {(x, j) | x ∈ ℝ}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓ j forms a labeling of the vertices. Such a graph G with the labeling φ is called an n-level graph and is said to be n-level planar if it can be drawn with straight-line edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are n-level planar regardless of their labeling. We call such trees unlabeled level planar (\(\sf{ULP}\)). Our contributions are three-fold. First, we provide a complete characterization of \(\sf{ULP}\) trees in terms of a pair of forbidden subtrees. Second, we show how to draw \(\sf{ULP}\) trees in linear time. Third, we provide a linear time recognition algorithm for \(\sf{ULP}\) trees.


Linear Time Degree Sequence Linear Time Algorithm Vertex Label Graph Drawing 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Alejandro Estrella-Balderrama
    • 1
  • J. Joseph Fowler
    • 1
  • Stephen G. Kobourov
    • 1
  1. 1.Department of Computer Science, University of Arizona 

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