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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Characterization of Unlabeled Level Planar Trees
verfasst von : Alejandro Estrella-Balderrama, J. Joseph Fowler, Stephen G. Kobourov
Erschienen in: Graph Drawing
Verlag: Springer Berlin Heidelberg
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Consider a graph
G
drawn in the plane so that each vertex lies on a distinct horizontal line ℓ
j
= {(
x
,
j
) |
x
∈ ℝ}. The bijection
φ
that maps the set of
n
vertices
V
to a set of distinct horizontal lines ℓ
j
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
(
$\sf{ULP}$
). Our contributions are three-fold. First, we provide a complete characterization of
$\sf{ULP}$
trees in terms of a pair of forbidden subtrees. Second, we show how to draw
$\sf{ULP}$
trees in linear time. Third, we provide a linear time recognition algorithm for
$\sf{ULP}$
trees.