\((g,f)\)-factorization orthogonal to a star in graphs
type: Item
instance of: scholarly article
title: \((g,f)\)-factorization orthogonal to a star in graphs
zbMATH Open document ID: 0841.05077
published in: Science in China. Series A
publication date: 1996-07-14T00:00:00Z
review text: The author proves the existence of a factorization of a graph into factors which are orthogonal to a special subgraph of \(G\). Let \(G= (V, E)\) be a graph, \(H\) a spanning subgraph of \(G\), \(g(v)\) and \(f(v)\) integer functions defined on \(V\) with the property that \(g(v)\leq \deg_H(v)\leq f(v)\) for every vertex \(v\). Then \(H\) is called a \((g, f)\)-factor of \(G\). A factorization of \(G\) is a decomposition \(F= (F_1, F_2,\dots, F_m)\) of \(G\) into factors. A factorization \(F\) is orthogonal to a subgraph \(H\) of \(G\), if \(|E(H)\cap E(F_i)|= 1\) for all \(i\). Let \(G\) be an \((mg+ m- 1, mf- m+ 1)\)-graph. The main result of the paper establishes the existence of an \((f, g)\)-factorization \(F\) orthogonal to a given \(m\)-star \(H\) of \(G\). This result is the best possible with respect to the boundaries of the degree \(\deg(v)\) in \(G\).
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 817803
zbMATH Keywords: star
zbMATH Keywords: factorization
zbMATH Keywords: factors
author: Guizhen Liu
reviewed by: Ludovit Niepel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 817803