Drawing graphs with vertices and edges in convex position - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Computational Geometry Année : 2016

Drawing graphs with vertices and edges in convex position

Résumé

A graph has strong convex dimension 2 if it admits a straight-line drawing in the plane such that its vertices form a convex set and the midpoints of its edges also constitute a convex set. Halman, Onn, and Rothblum conjectured that graphs of strong convex dimension 2 are planar and therefore have at most 3n − 6 edges. We prove that all such graphs have indeed at most 2n − 3 edges, while on the other hand we present an infinite family of non-planar graphs of strong convex dimension 2. We give lower bounds on the maximum number of edges a graph of strong convex dimension 2 can have and discuss several natural variants of this graph class. Furthermore, we apply our methods to obtain new results about large convex sets in Minkowski sums of planar point sets – a topic that has been of interest in recent years.
Fichier principal
Vignette du fichier
paper_rev.pdf (343.4 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01457727 , version 1 (06-02-2017)

Identifiants

Citer

Ignacio García-Marco, Kolja Knauer. Drawing graphs with vertices and edges in convex position. Computational Geometry, 2016, 58, pp.25-33. ⟨10.1016/j.comgeo.2016.06.002⟩. ⟨hal-01457727⟩
120 Consultations
556 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More