Low Ply Drawings of TreesAngelini, Patrizio and Bekos, Michael A. and Bruckdorfer, Till and Hančl Jr., Jaroslav and Kaufmann, Michael and Kobourov, Stephen G. and Symvonis, Antonios and Valtr, Pavel (2016) Low Ply Drawings of Trees. In: Graph Drawing and Network Visualization. GD 2016, September, 19.  21., 2016 , pp. 236248(Official URL: http://dx.doi.org/10.1007/9783319501062_19). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319501062_19
AbstractWe consider the recently introduced model of low ply graph drawing, in which the plydisks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The plydisk of a vertex in a straightline drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of plydisks having a common overlap is called the plynumber of the drawing. We focus on trees. We first consider drawings of trees with constant plynumber, proving that they may require exponential area, even for stars, and that they may not even exist for boundeddegree trees. Then, we turn our attention to drawings with logarithmic plynumber and show that trees with maximum degree 6 always admit such drawings in polynomial area.
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