On embeddings of snarks in the torus
type: Item
instance of: scholarly article
title: On embeddings of snarks in the torus
zbMATH Open document ID: 1154.05024
author: Andrej Vodopivec
published in: Discrete Mathematics
publication date: 2008-11-12T00:00:00Z
review text: In the paper, there is a condition on cubic graphs \(G_1\) and \(G_2\) , implying that a dot product \(G_1\cdot G_2\) has an embedding in the torus. Using this condition, it is proved that for every positive \(n\) there is a dot product of \(n\) copies of the Petersen graph, embeddable in the torus. This disproves a conjecture of Watkins and Tinsley and answers a question by Mohar.
reviewed by: Martin Knor
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 5365248
zbMATH Keywords: Snark
zbMATH Keywords: embedding in torus
zbMATH Keywords: cubic graph
zbMATH Keywords: dot product
zbMATH Keywords: Petersen graph
MaRDI profile type: Publication
full work available at URL: j.disc.2006.09.051
OpenAlex ID: W2149307464
cites work: Decomposition of snarks
cites work: Equivalence of Fleischner's and Thomassen's conjectures
cites work: Superposition and constructions of graphs without nowhere-zero \(k\)-flows
cites work: Q4821934
cites work: Q3222858
DOI: 10.1016/J.DISC.2006.09.051
Recommended article: Polyhedral embeddings of snarks in orientable surfaces
Recommended article: Polyhedral embeddings of snarks with arbitrary nonorientable genera
Recommended article: On embeddings of tori in Euclidean spaces
Recommended article: Q3788128
Recommended article: On the upward embedding on the torus
Recommended article: On the flexibility of toroidal embeddings
Recommended article: Torus embeddings and dualizing complexes
Recommended article: Cyclic covers and toroidal embeddings
Recommended article: Relating embedding and coloring properties of snarks
Recommended article: Toroidal embeddings and polyhedral divisors
description: scientific article; zbMATH DE number 5365248