The convex dimension of a graph

Nir Halman, Shmuel Onn, Uriel G. Rothblum

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The convex dimension of a graph G = (V, E) is the smallest dimension d for which G admits an injective map f : V {long rightwards arrow} Rd of its vertices into d-space, such that the barycenters of the images of the edges of G are in convex position. The strong convex dimension of G is the smallest d for which G admits a map as above such that the images of the vertices of G are also in convex position. In this paper we study the convex and strong convex dimensions of graphs.

Original languageEnglish
Pages (from-to)1373-1383
Number of pages11
JournalDiscrete Applied Mathematics
Volume155
Issue number11
DOIs
StatePublished - 1 Jun 2007
Externally publishedYes

Bibliographical note

Funding Information:
The research of the three authors was supported in part by a grant from ISF—the Israel Science Foundation.

Keywords

  • Convex combinatorial optimization
  • Discrete geometry
  • Graph embedding

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