On Vertex- and Empty-Ply Proximity Drawings
Abstract
We initiate the study of the vertex-ply of straight-line drawings, as a relaxation of the recently introduced ply number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-ply of a drawing is determined by the vertex covered by the maximum number of disks. The main motivation for considering this relaxation is to relate the concept of ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-ply number 1 can be seen as a weak proximity drawing, which we call empty-ply drawing. We show non-trivial relationships between the ply number and the vertex-ply number. Then, we focus on empty-ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the ply and the vertex-ply of planar drawings.
Cite
@article{arxiv.1708.09233,
title = {On Vertex- and Empty-Ply Proximity Drawings},
author = {Patrizio Angelini and Steven Chaplick and Felice De Luca and Jiri Fiala and Jaroslav Hancl and Niklas Heinsohn and Michael Kaufmann and Stephen Kobourov and Jan Kratochvil and Pavel Valtr},
journal= {arXiv preprint arXiv:1708.09233},
year = {2017}
}
Comments
Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017)