A note on zero-sum 5-flows in regular graphs
type: Item
instance of: scholarly article
title: A note on zero-sum 5-flows in regular graphs
zbMATH Open document ID: 1243.05100
author: S. Akbari
author: Narges Ghareghani
author: Gholamreza Khosrovshahi
author: S. Zare
published in: The Electronic Journal of Combinatorics
publication date: 2012-06-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1108.2950
full work available at URL: v19i2p7
review text: Summary: Let \(G\) be a graph. A zero-sum flow of \(G\) is an assignment of non-zero real numbers to the edges of \(G\) such that the sum of the values of all edges incident with each vertex is zero. Let \(k\) be a natural number. A zero-sum \(k\)-flow is a flow with values from the set \(\{\pm 1,\ldots ,\pm(k-1)\}\). It has been conjectured that every \(r\)-regular graph, \(r\geq 3\), admits a zero-sum 5-flow. In this paper we provide an affirmative answer to this conjecture, except for \(r=5\).
Mathematics Subject Classification ID: 05C21
Mathematics Subject Classification ID: 05C22
zbMATH DE Number: 6045700
zbMATH Keywords: zero-sum flow
zbMATH Keywords: regular graph
MaRDI profile type: Publication
arXiv ID: 1108.2950
description: scientific article; zbMATH DE number 6045700