Spanning sets and scattering sets in Steiner triple systems

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

Research output: Contribution to journalArticle

6 Scopus citations

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 - May 1991
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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