Group connectivity in line graphs
type: Item
instance of: scholarly article
title: Group connectivity in line graphs
zbMATH Open document ID: 1231.05118
author: Hong-Jian Lai
author: Hao Li
author: Ping Li
author: Yanting Liang
author: Senmei Yao
published in: Discrete Mathematics
publication date: 2011-10-21T00:00:00Z
review text: The authors study the Tutte-Jaeger conjecture and they prove the following theorem: (1) Every 5-edge-connected graph is \({\mathbb{Z}}_3\)-connected if and only if every 5-edge-connected line graph is \({\mathbb{Z}}_3\)-connected; (2) The following graphs are \({\mathbb{Z}}_3\)-connected and hence each has a nowhere zero 3-flow: 6-edge-connected triangular line graphs and 7-edge-connected triangular claw-free graphs.
Mathematics Subject Classification ID: 05C21
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C76
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 5961742
zbMATH Keywords: nowhere zero flows
zbMATH Keywords: group connectivity
zbMATH Keywords: line graphs
zbMATH Keywords: claw-free graphs
zbMATH Keywords: triangular graphs
reviewed by: Tongsuo Wu
MaRDI profile type: Publication
full work available at URL: j.disc.2011.07.017
OpenAlex ID: W2131724264
cites work: Q5570136
cites work: Q5422499
cites work: Q3070349
cites work: Nowhere zero flows in line graphs
cites work: Nowhere-zero 3-flows in triangularly connected graphs
cites work: Q5572939
cites work: Flows and generalized coloring theorems in graphs
cites work: Q3807237
cites work: Group connectivity of graphs --- a nonhomogeneous analogue of nowhere-zero flow properties
cites work: An equivalent version of the 3-flow conjecture
cites work: Group connectivity of 3-edge-connected chordal graphs
cites work: Nowhere‐zero 3‐flows in locally connected graphs
cites work: Every line graph of a 4-edge-connected graph is \(\mathbf Z_3\)-connected
cites work: On mod \((2p+1)\)-orientations of graphs
cites work: On group connectivity of graphs
cites work: Nowhere-zero 3-flows of highly connected graphs
cites work: On a closure concept in claw-free graphs
cites work: Nowhere-zero 6-flows
cites work: Nowhere-zero flows in random graphs
cites work: A Contribution to the Theory of Chromatic Polynomials
cites work: On the algebraic theory of graph colorings
cites work: Nowhere-zero 3-flows in squares of graphs
DOI: 10.1016/J.DISC.2011.07.017
description: scientific article; zbMATH DE number 5961742