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 (ULP). Our contributions are three-fold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Estrella-Balderrama, A., Fowler, J. J., & Kobourov, S. G. (2007). Characterization of unlabeled level planar trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4372 LNCS, pp. 367–379). Springer Verlag. https://doi.org/10.1007/978-3-540-70904-6_35
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