@inproceedings{56b1209a913741728cb77fc4b18c828c,

title = "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.",

author = "Patrizio Angelini and Steven Chaplick and Luca, {Felice De} and Fiara Jir{\'i} and Jr, {Jaroslav Hancl} and Niklas Heinsohn and Michael Kaufmann and Kobourov, {Stephen G.} and Jan Kratochv{\'i}l and Pavel Valtr",

note = "DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",

year = "2017",

doi = "10.1007/978-3-319-73915-1_3",

language = "English",

series = "Lecture Notes in Computer Science",

publisher = "Springer Nature Switzerland AG",

pages = "24--37",

editor = "F. Frati and KL Ma",

booktitle = "Graph Drawing and Network Visualization. GD 2017",

}