TY - GEN
T1 - Characterization of unlabeled level planar trees
AU - Estrella-Balderrama, Alejandro
AU - Fowler, J. Joseph
AU - Kobourov, Stephen G.
N1 - Funding Information:
✩ This work is supported in part by NSF grants CCF-0545743 and ACR-0222920.
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-540-70904-6_35
DO - 10.1007/978-3-540-70904-6_35
M3 - Conference contribution
AN - SCOPUS:38149033037
SN - 9783540709039
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 367
EP - 379
BT - Graph Drawing - 14th International Symposium, GD 2006, Revised Papers
PB - Springer-Verlag
T2 - 14th International Symposium on Graph Drawing, GD 2006
Y2 - 18 September 2006 through 19 September 2006
ER -