Cores and compactness of infinite directed graphs
type: Item
instance of: scholarly article
title: Cores and compactness of infinite directed graphs
zbMATH Open document ID: 0861.05028
author: Bruce L. Bauslaugh
published in: Journal of Combinatorial Theory. Series B
publication date: 1996-12-08T00:00:00Z
review text: We define the property of homomorphic compactness for digraphs. We prove that if a digraph \(H\) is homomorphically compact then \(H\) has a core, although the converse does not hold. We also examine a weakened compactness condition and show that when this condition is assumed, compactness is equivalent to containing a core. We use this result to prove that if a digraph \(H\) of size \(\kappa\) is not compact, then there is a digraph \(G\) of size at most \(\kappa^+\) such that \(H\) is not compact with respect to \(G\). We then give examples of some sufficient conditions for compactness.
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 954827
zbMATH Keywords: homomorphic compactness
zbMATH Keywords: digraphs
zbMATH Keywords: core
zbMATH Keywords: compact
MaRDI profile type: Publication
full work available at URL: jctb.1996.0068
OpenAlex ID: W2000020320
DOI: 10.1006/JCTB.1996.0068
description: scientific article; zbMATH DE number 954827