On a conjecture of A. Ainouche and N. Christofides
type: Item
instance of: scholarly article
title: On a conjecture of A. Ainouche and N. Christofides
zbMATH Open document ID: 0761.05065
author: Shijun Ren
author: Shengzheng Luo
published in: Chinese Science Bulletin
publication date: 1992-09-27T00:00:00Z
review text: Let \(a\) and \(b\) be two nonadjacent vertices of a 2-connected graph \(G=(V,E)\). Let \(T=\{x\in V\mid a,b\notin N(x)\}\) and let \(\lambda^ T_ i=|\{a_ j\in T\mid N(a_ j)\cap N(a_ i)\neq\varnothing\}|\). The following conjecture of Ainouche and Christofides is proved. Theorem: If \(d(a_ i)\geq 3+\lambda^ T_ i\) for all \(a_ i\in T\), then \(G\) is Hamiltonian if and only if \(G+ab\) is Hamiltonian.
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 62543
zbMATH Keywords: conjecture of Ainouche and Christofides
zbMATH Keywords: Hamiltonian
reviewed by: S. F. Kapoor
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 62543