Steiner triple systems with disjoint or intersecting subsystems

Charles J. Colbourn, Monica A. Oravas, Rolf S. Rees

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

The existence of incomplete Steiner triple systems of order v having holes of orders w and u meeting in z elements is examined, with emphasis on the disjoint (z = 0) and intersecting (z = 1) cases. When w ≥ u and v = 2w + u - 2z, the elementary necessary conditions are shown to be sufficient for all values of z. Then for z ∈ {0, 1} and v "near" the minimum of 2w + u - 2z, the conditions are again shown to be sufficient. Consequences for larger orders are also discussed, in particular the proof that when one hole is at least three times as large as the other, the conditions are again sufficient.

Original languageEnglish (US)
Pages (from-to)58-77
Number of pages20
JournalJournal of Combinatorial Designs
Volume8
Issue number1
DOIs
StatePublished - Jan 1 2000
Externally publishedYes

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Keywords

  • Incomplete pairwise balanced design
  • Steiner triple system

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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