TY - GEN

T1 - Low ply drawings of trees

AU - Angelini, Patrizio

AU - Bekos, Michael A.

AU - Bruckdorfer, Till

AU - Hančl, Jaroslav

AU - Kaufmann, Michael

AU - Kobourov, Stephen

AU - Symvonis, Antonios

AU - Valtr, Pavel

N1 - Funding Information:
An open access version of the full-text of the paper is also available []. Research partially supported by DFG grant Ka812/17-1. The research by Pavel Valtr was supported by the grant GAČR 14-14179S of the Czech Science Foundation.
Publisher Copyright:
© Springer International Publishing AG 2016.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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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U2 - 10.1007/978-3-319-50106-2_19

DO - 10.1007/978-3-319-50106-2_19

M3 - Conference contribution

AN - SCOPUS:85007290867

SN - 9783319501055

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 236

EP - 248

BT - Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers

A2 - Nollenburg, Martin

A2 - Hu, Yifan

PB - Springer-Verlag

T2 - 24th International Symposium on Graph Drawing and Network Visualization, GD 2016

Y2 - 19 September 2016 through 21 September 2016

ER -