# Characterization of Unlabeled Level Planar (ULP) Trees

Estrella-Balderrama, Alejandro and Fowler, J. Joseph and Kobourov, Stephen G. (2007) Characterization of Unlabeled Level Planar (ULP) Trees. In: Graph Drawing 14th International Symposium, GD 2006, September 18-20, 2006 , pp. 367-379(Official URL: http://dx.doi.org/10.1007/978-3-540-70904-6_35).

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## Abstract

Consider 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

Item Type: Conference Paper 10.1007/978-3-540-70904-6_35 Z Theory > Z.750 TopologyM Methods > M.900 Tree https://gdea.graphdrawing.org/id/eprint/792