Neighborhood unions and hamiltonicity of graphs
type: Item
instance of: scholarly article
title: Neighborhood unions and hamiltonicity of graphs
zbMATH Open document ID: 0833.05058
DOI: 10.1016/0012-365X(93)00181-4
author: Ruqun Shen
author: Feng Tian
published in: Discrete Mathematics
publication date: 1995-07-24T00:00:00Z
review text: If \(G\) is a 2-connected graph of order \(n\) such that the union of the neighborhoods of each pair of vertices that are a distance 2 apart is at least \((n+ 2)/3\), then \(G\) is either hamiltonian or belongs to one of three exceptional classes of graphs (all of which are 2-connected). This generalizes a result of \textit{B. Jackson} [J. Graph Theory 15, No. 4, 443- 451 (1991; Zbl 0739.05058)] in which the same neighborhood condition was used for all nonadjacent pairs of vertices.
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 778537
zbMATH Keywords: hamiltonicity
zbMATH Keywords: 2-connected graph
zbMATH Keywords: hamiltonian
zbMATH Keywords: neighborhood condition
reviewed by: Ralph Faudree
MaRDI profile type: Publication
cites work: Q5422499
cites work: A generalization of Ore's Theorem involving neighborhood unions
cites work: Neighbourhood unions and Hamiltonian properties in graphs
cites work: Neighborhood unions and hamilton cycles
cites work: The effects of distance and neighborhood union conditions on hamiltonian properties in graphs
full work available at URL: 0012-365x(93)00181-4
OpenAlex ID: W1964197500
description: scientific article; zbMATH DE number 778537