A new characterization of strongly chordal graphs
type: Item
instance of: scholarly article
title: A new characterization of strongly chordal graphs
zbMATH Open document ID: 0942.05060
DOI: 10.1016/S0012-365X(99)00107-7
author: Terry A. McKee
published in: Discrete Mathematics
publication date: 2000-08-15T00:00:00Z
review text: Define the strength of a set of edges as the number of inclusion-maximal complete subgraphs that contain it. The main result is that a graph is strongly chordal if and only if, for every \(k\geq 1\), every cycle of edges of strength at least \(k\) with no chord of strength at least \(k\) itself has strength at least \(k\). This approach being applied to the hereditary clique-Helly graphs provides that such a graph is strongly chordal if and only if, for every \(k\), the edges of strength at least \(k\) form a chordal graph.
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 1334694
zbMATH Keywords: chordal graphs
reviewed by: Sergej L. Bezrukov
MaRDI profile type: Publication
cites work: Characterizations of strongly chordal graphs
cites work: Topics in Intersection Graph Theory
cites work: Q4288086
cites work: Q3980562
full work available at URL: s0012-365x(99)00107-7
OpenAlex ID: W2087908433
Wikidata QID: Q127412172
description: scientific article; zbMATH DE number 1334694