Closure concepts: A survey
type: Item
instance of: scholarly article
title: Closure concepts: A survey
zbMATH Open document ID: 0946.05051
author: Zdeněk Ryjáček
author: Ingo Schiermeyer
author: Hajo Broersma
published in: Graphs and Combinatorics
publication date: 2000-10-18T00:00:00Z
review text: As the title indicates, this is a survey of results involving various types of closure conditions, where closure conditions involve adding an edge to a graph without changing the existence of some specified graphical property. Most of the graphical properties studied are hamiltonian type properties such as hamiltonian, panconnected, pancyclic, and cycle extendable, but other properties such as the existence of matchings are also studied. The Bondy-Chvátal closure, which started this line of investigation, is surveyed extensively along with the corresponding stability conditions. Results involving graphs with complete closures are also presented, as well as other related closure conditions such as the triple closure, \(0\)-dual closure, and neighborhood closure. For claw-free graphs, Ryjáček introduced a closure obtained by completing the neighborhoods of vertices with connected neighborhoods. Results using this closure are also described. This is a broad survey of ``closure'' results with an extensive list of references.
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05-02
zbMATH DE Number: 1436037
zbMATH Keywords: closure
zbMATH Keywords: Hamiltonian
reviewed by: Ralph Faudree
MaRDI profile type: Publication
full work available at URL: s003730050002
OpenAlex ID: W1992966703
DOI: 10.1007/S003730050002
description: scientific article; zbMATH DE number 1436037