Proceedings of the 30th Canadian Conference on Computational Geometry, CCCG 2018, August 8-10, 2018, University of Manitoba, Winnipeg, Manitoba, Canada

Ply number is a recently developed graph drawing metric inspired by studying road networks. Informally, for each vertex v, which is associated with a point in the plane, a disk is drawn centered on v with a radius that is α times the length of the longest edge incident to v, for some constant α ∈ (0, 0.5]. The ply number is the maximum number of disks that overlap at a single point. We show that any tree with maximum degree ∆ has a 1-ply drawing when α = O(1/∆). We also show that trees can be drawn with logarithmic ply number (for α = 0.5), with an area that is polynomial for boundeddegree trees. Lastly, we show that this logarithmic upper bound does not apply to 2-trees, by giving a lower bound of Ω( √ n/ log n) ply.