A note on Hamiltonicity of generalized net-free graphs of large diameter
type: Item
instance of: scholarly article
title: A note on Hamiltonicity of generalized net-free graphs of large diameter
zbMATH Open document ID: 1002.05043
DOI: 10.1016/S0012-365X(01)00327-2
author: Jan Brousek
author: Zdeněk Ryjáček
author: Ralph Faudree
published in: Discrete Mathematics
publication date: 2002-08-29T00:00:00Z
review text: A finite simple graph \(G\) is said to be \(\text{CN}_{i,j,k}\)-free if no induced subgraph is isomorphic to the claw \(K_{1,3}\) or to the graph \(N_{i,j,k}\) obtained by identifying each vertex of a 3-circuit with an endvertex of one of three disjoint nontrivial paths of lengths \(i\), \(j\), and \(k\), respectively. Main result: let \(G\) be 2-connected and let \(j\geq 2\) be an integer. Then \(G\) is Hamiltonian if either (1) \(G\) is \(\text{CN}_{1,2,j}\)-free and diam\((G)\geq\max\{7,2j\}\) or (2) \(G\) is \(\text{CN}_{1,1,j}\)-free and diam\((G)\geq\max\{4,2j\}\).
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 1792400
zbMATH Keywords: Hamiltonian
zbMATH Keywords: Hamiltonicity
zbMATH Keywords: diameter
zbMATH Keywords: generalized net
zbMATH Keywords: claw-free
reviewed by: Mark E. Watkins
MaRDI profile type: Publication
Wikidata QID: Q127642777
description: scientific article; zbMATH DE number 1792400