Smallest counterexample to the 5-flow conjecture has girth at least eleven
type: Item
instance of: scholarly article
title: Smallest counterexample to the 5-flow conjecture has girth at least eleven
zbMATH Open document ID: 1211.05055
author: Martin Kochol
published in: Journal of Combinatorial Theory. Series B
publication date: 2010-06-03T00:00:00Z
review text: A graph admits a nowhere-zero k-flow if its edges can be oriented and assigned numbers so that for every vertex, the sum of the values on incoming edges equals the sum on the outgoing ones. The famous 5-flow conjecture of Tutte is that every bridgeless graph has a nowhere-zero 5-flow. The paper shows that a smallest counterexample to this conjecture must have girth at least 11.
reviewed by: Wai-Kai Chen
Mathematics Subject Classification ID: 05C21
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 5716645
zbMATH Keywords: nowhere-zero 5-flow
zbMATH Keywords: girth
zbMATH Keywords: rank of a matrix
zbMATH Keywords: permutation group
MaRDI profile type: Publication
full work available at URL: j.jctb.2009.12.001
OpenAlex ID: W2003279860
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DOI: 10.1016/J.JCTB.2009.12.001
description: scientific article; zbMATH DE number 5716645