Spanning sets and scattering sets in Steiner triple systems

Charles Colbourn, Jeffrey H. Dinitz, Douglas R. Stinson

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A spanning set in a Steiner triple system is a set of elements for which each element not in the spanning set appears in at least one triple with a pair of elements from the spanning set. A scattering set is a set of elements that is independent, and for which each element not in the scattering set is in at most one triple with a pair of elements from the scattering set. For each v ≡ 1, 3 (mod 6), we exhibit a Steiner triple system with a spanning set of minimum cardinality, and a Steiner triple system with a scattering set of maximum cardinality. In the process, we establish the existence of Steiner triple systems with complete arcs of the minimum possible cardinality.

Original languageEnglish (US)
Pages (from-to)46-59
Number of pages14
JournalJournal of Combinatorial Theory, Series A
Volume57
Issue number1
DOIs
StatePublished - 1991
Externally publishedYes

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Steiner Triple System
Scattering
Cardinality
Arc of a curve

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Spanning sets and scattering sets in Steiner triple systems. / Colbourn, Charles; Dinitz, Jeffrey H.; Stinson, Douglas R.

In: Journal of Combinatorial Theory, Series A, Vol. 57, No. 1, 1991, p. 46-59.

Research output: Contribution to journalArticle

Colbourn, Charles ; Dinitz, Jeffrey H. ; Stinson, Douglas R. / Spanning sets and scattering sets in Steiner triple systems. In: Journal of Combinatorial Theory, Series A. 1991 ; Vol. 57, No. 1. pp. 46-59.
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