### 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(λυ^{2} + 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 ≥ 6λv^{2} + 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 language | English (US) |
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Pages (from-to) | 363-369 |

Number of pages | 7 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 37 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Combinatorial Theory, Series A*,

*37*(3), 363-369. https://doi.org/10.1016/0097-3165(84)90059-1