Small embeddings of partial directed triple systems and partial triple systems with even λ

Charles J. Colbourn, Rose C. Hamm, C. A. Rodger

Research output: Contribution to journalArticle

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Abstract

In 1976, Lindner and Rosa (Ars Combin. 1 (1976), 159-166) showed that a partial triple system with λ > 1 can be embedded in a finite triple system with the same λ. This result is improved in the case when λ is even by embedding a partial triple system on υ symbols in a triple system on t symbols, t ≡ 0,1 (mod 3), for all t >/ 3(λυ2 + υ(2 - λ) + 1). In the process, it is shown that for any λ >/ 1, a partial directed triple system on υ symbols can be embedded in a directed triple system on t symbols, t ≡ 0, 1 (mod 3), for all t ≥ 6λv2 + 6v(1 - λ) + 3, thus generalizing a result of Hamm (Proceedings, 14th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, Boca Raton, Florida, 1983).

Original languageEnglish (US)
Pages (from-to)363-369
Number of pages7
JournalJournal of Combinatorial Theory, Series A
Volume37
Issue number3
DOIs
StatePublished - Nov 1984
Externally publishedYes

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ASJC Scopus subject areas

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

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