On vertex- and empty-ply proximity drawings

Patrizio Angelini, Steven Chaplick, Felice De Luca, Jiří Fiala, Jaroslav Hančl, Niklas Heinsohn, Michael Kaufmann, Stephen Kobourov, Jan Kratochvíl, Pavel Valtr

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

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 (US)
Title of host publicationGraph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers
EditorsKwan-Liu Ma, Fabrizio Frati
PublisherSpringer-Verlag
Pages24-37
Number of pages14
ISBN (Print)9783319739144
DOIs
StatePublished - 2018
Event25th International Symposium on Graph Drawing and Network Visualization, GD 2017 - Boston, United States
Duration: Sep 25 2017Sep 27 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10692 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other25th International Symposium on Graph Drawing and Network Visualization, GD 2017
CountryUnited States
CityBoston
Period9/25/179/27/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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