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 ℓj = {(x, j) | x ∈ ℝ}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj 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.


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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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