Further 6-sparse Steiner triple systems
type: Item
instance of: scholarly article
title: Further 6-sparse Steiner triple systems
zbMATH Open document ID: 1188.05034
published in: Graphs and Combinatorics
publication date: 2009-12-09T00:00:00Z
review text: Erdös conjectured that for each \(k\geq 4\) there exists \(v(k)\) so that for every admissible \(v>v(k)\) there exists a Steiner Triple System on \(v\) points, \(STS(v),\) which does contains no configuration having \(n\) blocks on \(n+2\) points for \(n\) with \(4\leq n\leq k.\) Such \(STS(v)\) is called to be \(k\)-sparse. The existence of \(4\)-sparse systems for all admissible values of \(v,\) and the existence of \(5\)-sparse systems for almost all admissible values of \( v\) has been established. In this paper the authors construct a \(6\)-sparse \(STS(v)\) for \(v=3p,\) where \(p\) is sufficiently big prime \(p\equiv 3\pmod {4}\).
reviewed by: Peter Horák
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 5644622
zbMATH Keywords: Steiner triple system
zbMATH Keywords: 6-sparse
zbMATH Keywords: Pash configuration
zbMATH Keywords: Mitre configuration
author: Anthony D. Forbes
author: Michael John Grannell
author: T. S. Griggs
MaRDI profile type: Publication
full work available at URL: s00373-008-0819-3
OpenAlex ID: W2039518752
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DOI: 10.1007/S00373-008-0819-3
description: scientific article; zbMATH DE number 5644622