Infinite friendship graphs with infinite parameters
type: Item
instance of: scholarly article
title: Infinite friendship graphs with infinite parameters
zbMATH Open document ID: 0707.05058
DOI: 10.1016/0095-8956(91)90087-Z
author: Geňa Hahn
author: Eric C. Milner
author: R. E. Woodrow
published in: Journal of Combinatorial Theory. Series B
publication date: 1991-01-01T00:00:00Z
review text: We study infinite graphs in which every set of \(\kappa\) vertices has exactly \(\lambda\) common neighbours. We prove that there exist \(2^{\sigma}\) such graphs of each infinite order \(\sigma\) if \(\kappa\) is finite and that for \(\kappa\) infinite there are \(2^{\lambda}\) of them of order \(\lambda\) and none of cardinality greater than \(\lambda\) (assuming the GCH). Further, we show that all a priori admissible chromatic numbers are in fact possible for such graphs.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 4160791
zbMATH Keywords: almost disjoint sets
zbMATH Keywords: friendship graph
zbMATH Keywords: infinite graphs
zbMATH Keywords: common neighbours
zbMATH Keywords: chromatic numbers
MaRDI profile type: Publication
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full work available at URL: 0095-8956(91)90087-z
OpenAlex ID: W2057800980
description: scientific article; zbMATH DE number 4160791