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.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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 -