Simple neighbourhoods in triple systems

Charles J. Colbourn

doi:10.1016/0097-3165(89)90058-7

Simple neighbourhoods in triple systems

Charles J. Colbourn

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The neighbourhood of an element in a triple system of index λ is the λ-regular multigraph whose edges are the unordered pairs appearing in triples with the fixed element. We prove, for every λ, that every λ-regular simple graph meeting the necessary congruence and density conditions appears as the neighbourhood of an element. Applications in design theory are given.

Original language	English (US)
Pages (from-to)	10-19
Number of pages	10
Journal	Journal of Combinatorial Theory, Series A
Volume	52
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(89)90058-7
State	Published - Sep 1989
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0097-3165(89)90058-7

Cite this

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title = "Simple neighbourhoods in triple systems",

abstract = "The neighbourhood of an element in a triple system of index λ is the λ-regular multigraph whose edges are the unordered pairs appearing in triples with the fixed element. We prove, for every λ, that every λ-regular simple graph meeting the necessary congruence and density conditions appears as the neighbourhood of an element. Applications in design theory are given.",

author = "Colbourn, \{Charles J.\}",

note = "Funding Information: Thanks to Brendan McKay and Alex Rosa for helpful discussions. This research was partially supported by NSERC Canada under Grant A0579 and was undertaken in part while visiting at the University of Auckland.",

year = "1989",

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N1 - Funding Information: Thanks to Brendan McKay and Alex Rosa for helpful discussions. This research was partially supported by NSERC Canada under Grant A0579 and was undertaken in part while visiting at the University of Auckland.

PY - 1989/9

Y1 - 1989/9

N2 - The neighbourhood of an element in a triple system of index λ is the λ-regular multigraph whose edges are the unordered pairs appearing in triples with the fixed element. We prove, for every λ, that every λ-regular simple graph meeting the necessary congruence and density conditions appears as the neighbourhood of an element. Applications in design theory are given.

AB - The neighbourhood of an element in a triple system of index λ is the λ-regular multigraph whose edges are the unordered pairs appearing in triples with the fixed element. We prove, for every λ, that every λ-regular simple graph meeting the necessary congruence and density conditions appears as the neighbourhood of an element. Applications in design theory are given.

UR - https://www.scopus.com/pages/publications/38249005103

UR - https://www.scopus.com/pages/publications/38249005103#tab=citedBy

U2 - 10.1016/0097-3165(89)90058-7

DO - 10.1016/0097-3165(89)90058-7

M3 - Article

AN - SCOPUS:38249005103

SN - 0097-3165

VL - 52

SP - 10

EP - 19

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

IS - 1

ER -

Simple neighbourhoods in triple systems

Abstract

ASJC Scopus subject areas

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