The convex dimension of a graph

Nir Halman; Shmuel Onn; Uriel G. Rothblum

doi:10.1016/j.dam.2007.02.005

The convex dimension of a graph

Nir Halman, Shmuel Onn, Uriel G. Rothblum

Research output: Contribution to journal › Article › peer-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} R^d 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 language	English
Pages (from-to)	1373-1383
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	155
Issue number	11
DOIs	https://doi.org/10.1016/j.dam.2007.02.005
State	Published - 1 Jun 2007
Externally published	Yes

Bibliographical note

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

Funding

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

Funders	Funder number
Israel Science Foundation

Keywords

Convex combinatorial optimization
Discrete geometry
Graph embedding

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10.1016/j.dam.2007.02.005

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The convex dimension of a graph

Abstract

Bibliographical note

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Keywords

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