Embedding products into symmetric products of finite graphs
type: Item
instance of: scholarly article
title: Embedding products into symmetric products of finite graphs
zbMATH Open document ID: 1398.54053
author: Florencio Corona-Vázquez
author: Hugo Villanueva
author: Russell-Aarón Quiñones-Estrella
author: Javier Sánchez-Martínez
published in: Topology and its Applications
publication date: 2018-06-25T00:00:00Z
review text: The question treated in the paper, under the usual notation, is the embeddability of the product \(X^n\) into the symmetric product \(F_n(X)\) when \(X\) is a finite graph. It has been proved previously that if \(X\) is a finite graph, then \(X^2\) can be embedded into \(F_2(X)\) iff \(X\) is an arc. The obtained result says that the same statement holds for \(n=3\). So the following holds: If \(X\) is a finite graph, then \(X^3\) can be embedded into \(F_3(X)\) iff \(X\) is an arc. Besides some other results, at the end of the paper the authors construct a geometric model for \(F_3(Y)\), where \(Y\) is a simple triod.
reviewed by: Ivan Ivanšić
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 6894000
zbMATH Keywords: embedding
zbMATH Keywords: product
zbMATH Keywords: symmetric product
zbMATH Keywords: finite graph
MaRDI profile type: Publication
full work available at URL: j.topol.2018.04.003
OpenAlex ID: W2795836998
cites work: Q5692771
cites work: Embedding products in symmetric products of continua
cites work: On the symmetric hyperspace of the circle
cites work: Models of hyperspaces
cites work: Q4819417
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DOI: 10.1016/J.TOPOL.2018.04.003
Wikidata QID: Q130021803
description: scientific article; zbMATH DE number 6894000