Element neighbourhoods in twofold triple systems
type: Item
instance of: scholarly article
title: Element neighbourhoods in twofold triple systems
zbMATH Open document ID: 0624.05011
DOI: 10.1007/BF01223261
author: Charles J. Colbourn
author: Alexander Rosa
published in: Journal of Geometry
publication date: 1987-01-01T00:00:00Z
review text: A twofold triple system TTS(v) is a (v,3,2)-design. The neighbourhood N(p) of the point p is the multigraph on \(V\setminus \{p\}\) (V the point set) with an edge \(\{\) x,y\(\}\) for every block \(\{\) p,x,y\(\}\) through p. Thus N(p) is a 2-regular multigraph on v-1 vertices. The authors prove that every 2-regular multigraph on \(n\equiv 0\) or 2 (mod 3) vertices occurs as a neighbourhood graph in a TTS, with two exceptions (vis. \(C_ 2\cup C_ 3\) and \(C_ 3\cup C_ 3)\). The proof uses difference methods.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4012623
zbMATH Keywords: twofold triple system
zbMATH Keywords: TTS
zbMATH Keywords: neighbourhood
MaRDI profile type: Publication
cites work: Q3342583
cites work: Completing small partial triple systems
cites work: Quadratic leaves of maximal partial triple systems
cites work: Les G-Systemes Triples
cites work: Q5545293
cites work: Q4175291
cites work: Langford sequences: Perfect and hooked
full work available at URL: https://doi.org/10.1007/bf01223261
OpenAlex ID: W2063853921
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description: scientific article; zbMATH DE number 4012623