Cubic Neighbourhoods in Triple Systems

Charles J. Colbourn; Brendan D. McKay

doi:10.1016/S0304-0208(08)72880-9

Cubic Neighbourhoods in Triple Systems

Charles J. Colbourn
, Brendan D. McKay

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

1 Scopus citations

Abstract

In a triple system of index 3, the multiset of pairs appearing in triples with a fixed element form a cubic multigraph called the neighbourhood of the element. We prove that, with precisely three exceptions, every cubic multigraph appears as an element neighbourhood in a triple system. The proof technique involves establishing the existence of certain path factorizations of cubic graphs.

Original language	English (US)
Pages (from-to)	119-136
Number of pages	18
Journal	North-Holland Mathematics Studies
Volume	149
Issue number	C
DOIs	https://doi.org/10.1016/S0304-0208(08)72880-9
State	Published - Jan 1987
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1016/S0304-0208(08)72880-9

Cite this

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title = "Cubic Neighbourhoods in Triple Systems",

abstract = "In a triple system of index 3, the multiset of pairs appearing in triples with a fixed element form a cubic multigraph called the neighbourhood of the element. We prove that, with precisely three exceptions, every cubic multigraph appears as an element neighbourhood in a triple system. The proof technique involves establishing the existence of certain path factorizations of cubic graphs.",

author = "Colbourn, \{Charles J.\} and McKay, \{Brendan D.\}",

note = "Funding Information: Thanks to Alex Rosa, and to the referee, for helpful comments. also acknowledges the financial support of NSERC Canada.",

year = "1987",

month = jan,

doi = "10.1016/S0304-0208(08)72880-9",

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AU - Colbourn, Charles J.

AU - McKay, Brendan D.

N1 - Funding Information: Thanks to Alex Rosa, and to the referee, for helpful comments. also acknowledges the financial support of NSERC Canada.

PY - 1987/1

Y1 - 1987/1

N2 - In a triple system of index 3, the multiset of pairs appearing in triples with a fixed element form a cubic multigraph called the neighbourhood of the element. We prove that, with precisely three exceptions, every cubic multigraph appears as an element neighbourhood in a triple system. The proof technique involves establishing the existence of certain path factorizations of cubic graphs.

AB - In a triple system of index 3, the multiset of pairs appearing in triples with a fixed element form a cubic multigraph called the neighbourhood of the element. We prove that, with precisely three exceptions, every cubic multigraph appears as an element neighbourhood in a triple system. The proof technique involves establishing the existence of certain path factorizations of cubic graphs.

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U2 - 10.1016/S0304-0208(08)72880-9

DO - 10.1016/S0304-0208(08)72880-9

M3 - Article

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EP - 136

JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

IS - C

ER -

Cubic Neighbourhoods in Triple Systems

Abstract

ASJC Scopus subject areas

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