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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Low Ply Drawings of Trees
verfasst von : Patrizio Angelini, Michael A. Bekos, Till Bruckdorfer, Jaroslav Hančl Jr., Michael Kaufmann, Stephen Kobourov, Antonios Symvonis, Pavel Valtr
Erschienen in: Graph Drawing and Network Visualization
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Abstract
We consider the recently introduced model of low ply graph drawing, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the ply-number of the drawing.
We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree 6 always admit such drawings in polynomial area.