A characterization of graphs having all \((g,f)\)-factors
type: Item
instance of: scholarly article
title: A characterization of graphs having all \((g,f)\)-factors
zbMATH Open document ID: 0888.05048
published in: Journal of Combinatorial Theory. Series B
publication date: 1997-09-15T00:00:00Z
review text: Let \(G\) be a graph with vertex set \(V\) and let \(g,f:V\to\mathbb{Z}^+\). We say that \(G\) has all \((g,f)\)-factors, if \(G\) has an \(h\)-factor for every \(h:V\to\mathbb{Z}^+\) such that \(g(v)\leq h(v)\leq f(v)\) for every \(v\in V\) and at least one such \(h\) exists. We derive from Tutte's \(f\)-factor theorem a similar characterization for the property of having all \((g,f)\)-factors. An analogous result for parity factors is presented also.
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 1060754
zbMATH Keywords: characterization
zbMATH Keywords: \((g,f)\)-factors
zbMATH Keywords: parity factors
author: Thomas Niessen
MaRDI profile type: Publication
full work available at URL: jctb.1997.1797
OpenAlex ID: W2012934650
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DOI: 10.1006/JCTB.1997.1797
description: scientific article; zbMATH DE number 1060754