## Abstract A well‐known, and unresolved, conjecture states that every partial Steiner triple system of order __u__ can be embedded in a Steiner triple system of order υ for all υ ≡ 1 or 3, (mod 6), υ ≥ 2u + 1. However, some partial Steiner triple systems of order __u__ can be embedded in Steiner t
Small embeddings of partial directed triple systems and partial triple systems with even λ
✍ Scribed by Charles J Colbourn; Rose C Hamm; C.A Rodger
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 375 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0097-3165
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📜 SIMILAR VOLUMES
## Abstract It is proved in this article that the necessary and sufficient conditions for the embedding of a λ‐fold pure Mendelsohn triple system of order __v__ in λ‐__fold__ pure Mendelsohn triple of order __u__ are λ__u__(__u__ − 1) ≡ 0 (mod 3) and __u__ ⩾ 2__v__ + 1. Similar results for the embe
## Abstract Lindner's conjecture that any partial Steiner triple system of order __u__ can be embedded in a Steiner triple system of order __v__ if $v\equiv 1,3 \; ({\rm mod}\; 6)$ and $v\geq 2u+1$ is proved. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 63–89, 2009
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