On Vertex- and Empty-Ply Proximity Drawings

Patrizio Angelini, Steven Chaplick, Felice De Luca, Fiara Jirí, Jaroslav Hancl Jr, Niklas Heinsohn, Michael Kaufmann, Stephen G. Kobourov, Jan Kratochvíl, Pavel Valtr

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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.
Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization. GD 2017
EditorsF. Frati, KL Ma
Pages24-37
DOIs
Publication statusPublished - 2017
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science
Volume10692
ISSN0302-9743

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