Characterization of Unlabeled Level Planar (ULP) TreesEstrellaBalderrama, 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 1820, 2006 , pp. 367379(Official URL: http://dx.doi.org/10.1007/9783540709046_35). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783540709046_35
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 nlevel graph and is said to be nlevel planar if it can be drawn with straightline edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are nlevel planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are threefold. 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
Actions (login required)
