Closure and Hamiltonian-connectivity of claw-free graphs
type: Item
instance of: scholarly article
title: Closure and Hamiltonian-connectivity of claw-free graphs
zbMATH Open document ID: 0933.05085
DOI: 10.1016/S0012-365X(98)00165-4
author: Béla Bollobás
author: Oliver Riordan
author: Zdeněk Ryjáček
author: Akira Saito
author: R. H. Schelp
published in: Discrete Mathematics
publication date: 1999-11-02T00:00:00Z
review text: The authors define for a graph \(G\), a new closure \(\text{cl}_k(G)\) \((k\geq 1)\) as a generalization of \(\text{cl}(G)\) and prove the following results: (1) A claw-free graph \(G\) is Hamiltonian-connected iff \(\text{cl}_3(G)\) is Hamiltonian-connected. (2) A claw-free graph \(G\) is homogeneously traceable iff \(\text{cl}_2(G)\) is homogeneously traceable. The uniqueness of the closure has also been discussed. Finally, they make the following conjecture: A claw-free graph \(G\) is Hamiltonian-connected iff \(\text{cl}_2(G)\) is Hamiltonian-connected.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 1320577
zbMATH Keywords: Hamiltonian-connected graph
zbMATH Keywords: closure
zbMATH Keywords: claw-free graph
reviewed by: Bai Kishan Dass
MaRDI profile type: Publication
cites work: Closure and stable Hamiltonian properties in claw-free graphs
cites work: Q3818315
cites work: On a closure concept in claw-free graphs
cites work: Graphs with 1-Factors
description: scientific article; zbMATH DE number 1320577