### 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 language | English (US) |
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Pages (from-to) | 46-59 |

Number of pages | 14 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - May 1991 |

Externally published | Yes |

### ASJC Scopus subject areas

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

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## Cite this

*Journal of Combinatorial Theory, Series A*,

*57*(1), 46-59. https://doi.org/10.1016/0097-3165(91)90004-Z