Graph decompositions without isolated vertices
type: Item
instance of: scholarly article
title: Graph decompositions without isolated vertices
zbMATH Open document ID: 0834.05046
author: Hikoe Enomoto
published in: Journal of Combinatorial Theory. Series B
publication date: 1995-07-02T00:00:00Z
review text: The author proves the following conjecture of \textit{A. Frank} (Fifth British Combinatorial Conference, Aberdeen, Scotland, 1975): Let \(G\) be a connected simple graph of order \(n\), and \(n= n_1+\cdots+ n_k\) be a partition of \(n\) with \(n\geq 2\). Suppose that the minimum degree of \(G\) is at least \(k\). Then the vertex set \(V(G)\) can be decomposed into disjoint subsets \(V_1,\dots, V_k\) so that \(|V_i|= n_i\) and the subgraph induced by \(V_i\) contains no isolated vertices for all \(i\), \(1\leq i\leq k\).
reviewed by: Katherine Heinrich
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 767682
zbMATH Keywords: graph decompositions
zbMATH Keywords: partition
zbMATH Keywords: isolated vertices
MaRDI profile type: Publication
full work available at URL: jctb.1995.1007
OpenAlex ID: W2012829609
DOI: 10.1006/JCTB.1995.1007
description: scientific article; zbMATH DE number 767682