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Blocking Sets in SQS(2v)

Published online by Cambridge University Press:  12 September 2008

Mario Gionfriddo ,
Salvatore Milici  and
Zsolt Tuza
Mario Gionfriddo
Affiliation:
Dipartimento di Matematica, Città Universitaria, Viale A, Doria 6, 95125 Catania, Italy.
Salvatore Milici
Affiliation:
Dipartimento di Matematica, Città Universitaria, Viale A, Doria 6, 95125 Catania, Italy.
Zsolt Tuza
Affiliation:
Computer and Automation Institute, Hungarian Academy of Sciences, H-llll Budapest, Kende u. 13–17, Hungary
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Abstract

A Steiner quadruple system SQS(v) of order v is a family ℬ of 4-element subsets of a v-element set V such that each 3-element subset of V is contained in precisely one B ∈ ℬ. We prove that if T ∩ B ≠ ø for all B ∈ ℬ (i.e., if T is a transversal), then |T| ≥ v/2, and if T is a transversal of cardinality exactly v/2, then V \ T is a transversal as well (i.e., T is a blocking set). Also, in respect of the so-called ‘doubling construction’ that produces SQS(2v) from two copies of SQS(v), we give a necessary and sufficient condition for this operation to yield a Steiner quadruple system with blocking sets.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 77 - 86
Copyright
Copyright © Cambridge University Press 1994

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References

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