1 research outputs found
Low Ply Drawings of Trees and 2-Trees
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 alpha times
the length of the longest edge incident to v, for some constant alpha in (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 Delta has a 1-ply drawing when
alpha = O(1 / Delta). We also show that when alpha = 1/2, trees can be drawn
with logarithmic ply number, with an area that is polynomial for bounded-degree
trees. Lastly, we show that this logarithmic upper bound does not apply to
2-trees, by giving a lower bound of Omega(sqrt(n / log n)) ply for any value of
alpha