Disproofs of generalized Gilbert-Pollak conjecture on the Steiner ratio in three or more dimensions
type: Item
instance of: scholarly article
title: Disproofs of generalized Gilbert-Pollak conjecture on the Steiner ratio in three or more dimensions
zbMATH Open document ID: 0856.05025
author: Du Ding-Zhu
author: Warren D. Smith
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-07-09T00:00:00Z
review text: The generalized Gilbert-Pollak conjecture states that the ratio \(\ell_{\text{SMT}} (P)/ \ell_{\text{MST}} (P)\), where SMT is the Steiner minimal tree and MST the minimum spanning tree of a point set \(P\), is achieved when \(P\) is the set of vertices of a regular \(d\)-simplex. The authors give an ultra-simplified disproof for \(d \geq 3\) (for \(d = 2\) the conjecture is true) and introduce the concept of ``\(d\)-dimensional'' sausage point sets which seem to have to do with the true minimal ratio point sets.
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 883804
zbMATH Keywords: Steiner trees
zbMATH Keywords: Steiner ratio
zbMATH Keywords: Gilbert-Pollak conjecture
zbMATH Keywords: spanning tree
reviewed by: Peter Kirschenhofer
MaRDI profile type: Publication
full work available at URL: jcta.1996.0040
OpenAlex ID: W2094055387
Wikidata QID: Q123115171
DOI: 10.1006/JCTA.1996.0040
description: scientific article; zbMATH DE number 883804