## Characterization of Unlabeled Level Planar (ULP) Trees
Estrella-Balderrama, Alejandro and Fowler, J. Joseph and Kobourov, Stephen G.
(2007)
Full text not available from this repository. ## AbstractConsider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line $\ell_j = \{(x, j) \,|\, x \in \BB{R}\}$. The bijection $\phi$ that maps the set of n vertices V to a set of distinct horizontal lines $\ell_j$\isTR{ for $j\in \{1,2,\ldots,n\}$ forms a labeling of the vertices. Such a graph G with the labeling $\phi$ 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.n
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