Discs in unbreakable graphs
type: Item
instance of: scholarly article
title: Discs in unbreakable graphs
zbMATH Open document ID: 0833.05032
DOI: 10.1007/BF01793011
author: Ryan Hayward
published in: Graphs and Combinatorics
publication date: 1996-03-11T00:00:00Z
review text: A graph \(G\) is said to be unbreakable if it has at least three vertices and neither the graph nor its complement has a star cutset (i.e., a non- empty subset \(C\) of the vertices of \(G\), for which \(G- C\) is disconnected and some vertex of \(C\) is adjacent to all other vertices of \(C\)). In this paper it is shown that every vertex in an unbreakable graph is in a disc, where a disc is a chordless cycle, or the complement of a chordless cycle, with at least five vertices. A corollary is that every vertex in a minimal imperfect graph is in a disc.
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C60
zbMATH DE Number: 811345
zbMATH Keywords: perfect graph
zbMATH Keywords: unbreakable graph
zbMATH Keywords: disc
zbMATH Keywords: chordless cycle
reviewed by: Ioan Tomescu
MaRDI profile type: Publication
cites work: Q3286847
cites work: Topics on perfect graphs
cites work: Star-cutsets and perfect graphs
cites work: Weakly triangulated graphs
full work available at URL: https://doi.org/10.1007/bf01793011
OpenAlex ID: W2016193533
description: scientific article; zbMATH DE number 811345