# Low Ply Drawings of Trees

• Patrizio Angelini
• Michael A. Bekos
• Till Bruckdorfer
• Jaroslav HančlJr.
• Michael Kaufmann
• Stephen Kobourov
• Antonios Symvonis
• Pavel Valtr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

## 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.

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© Springer International Publishing AG 2016

## Authors and Affiliations

• Patrizio Angelini
• 1
• Michael A. Bekos
• 1
Email author
• Till Bruckdorfer
• 1
• Jaroslav HančlJr.
• 2
• Michael Kaufmann
• 1
• Stephen Kobourov
• 3
• Antonios Symvonis
• 4
• Pavel Valtr
• 2
1. 1.Institut für InformatikUniversität TübingenTübingenGermany
2. 2.Department of Applied MathematicsCharles University (KAM)PragueCzech Republic
3. 3.Department for Computer ScienceUniversity of ArizonaTucsonUSA
4. 4.School of Applied Mathematical and Physical SciencesNTUAAthensGreece