On constructible graphs, infinite bridged graphs and weakly cop-win graphs
type: Item
instance of: scholarly article
title: On constructible graphs, infinite bridged graphs and weakly cop-win graphs
zbMATH Open document ID: 0961.05066
DOI: 10.1016/S0012-365X(00)00127-8
author: Marc Chastand
author: François Laviolette
author: Norbert Polat
published in: Discrete Mathematics
publication date: 2001-03-05T00:00:00Z
review text: It is proved that all Helly graphs and connected bridged graphs are constructible. New characterizations of bridged graphs have been deduced. It is also proved that any connected bridged graph is `moorable', a property which implies various fixed point properties. Further, a problem of Hahn et al. has been solved by proving that any finite subgraph of a bridged (resp. constructible) graph \(G\) is contained in a finite induced subgraph \(K\) of \(G\) which is bridged (resp. constructible). It is also shown that the vertex set of \(K\) is a geodesically convex subset of \(V(G)\) whenever \(G\) is locally finite or contains no infinite paths. Some relations between constructible graphs and a weakening of the concept of cop-win graph have been studied.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 1533339
zbMATH Keywords: Helly graph
zbMATH Keywords: bridged graph
zbMATH Keywords: characterizations
zbMATH Keywords: constructible graphs
zbMATH Keywords: cop-win graph
MaRDI profile type: Publication
full work available at URL: s0012-365x(00)00127-8
OpenAlex ID: W2011663983
description: scientific article; zbMATH DE number 1533339