A new extremal property of Steiner triple-systems

P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Suppose S is a Steiner triple-system on the n-element set X, i.e., for every pair of distinct vertices of X there is exactly one triple in S containing them. Necessarily, |S| = n(n - 1)/6 holds. It is easy to see that, for S, T, S′, T′ ∈ S, S ∪ T = S′ ∪ T′ implies {S, T} = {S′, T′}. We show that, conversely, this condition, for any family S′ of 3-subsets of X, implies |S′| ≤ n(n - 1)/6. A similar type of result is obtained for a weaker union condition. The corresponding problems for graphs are still open.

Original languageEnglish
Pages (from-to)205-212
Number of pages8
JournalDiscrete Mathematics
Volume48
Issue number2-3
DOIs
Publication statusPublished - 1984

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

A new extremal property of Steiner triple-systems. / Frankl, P.; Füredi, Z.

In: Discrete Mathematics, Vol. 48, No. 2-3, 1984, p. 205-212.

Research output: Contribution to journalArticle

Frankl, P. ; Füredi, Z. / A new extremal property of Steiner triple-systems. In: Discrete Mathematics. 1984 ; Vol. 48, No. 2-3. pp. 205-212.
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