### Abstract

A (K_{4} - e)-design of order v + w embeds a given Steiner triple system if there is a subset of v points on which the graphs of the design induce the blocks of the original Steiner triple system. It has been established that w ≥ v / 3, and that when equality is met, such a minimum embedding of an STS(v) exists, except when v = 15. Equality only holds when v ≡ 15, 27 (mod 30). One natural question is: What is the smallest order w such that some STS(v) can be embedded into a (K_{4} - e)-design of order v + w? We solve the problem for 7 of the 10 congruence classes modulo 30.

Original language | English (US) |
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Pages (from-to) | 400-411 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 2 |

DOIs | |

State | Published - Jan 28 2009 |

### Keywords

- Embedding

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Ling, A. C. H., Colbourn, C., & Quattrocchi, G. (2009). Minimum embedding of Steiner triple systems into (K

_{4}- e)-designs II.*Discrete Mathematics*,*309*(2), 400-411. https://doi.org/10.1016/j.disc.2007.12.026