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- W2952380475 abstract "It was proved in 2009 that any partial Steiner triple system of order $u$ has an embedding of order $v$ for each admissible integer $vgeq 2u+1$. This result is best-possible in the sense that, for each $ugeq 9$, there exists a partial Steiner triple system of order $u$ that does not have an embedding of order $v$ for any $v<2u+1$. Many partial Steiner triple systems do have embeddings of orders smaller than $2u+1$, but little has been proved about when these embeddings exist. In this paper we construct embeddings of orders less than $2u+1$ for partial Steiner triple systems with few triples. In particular, we show that a partial Steiner triple system of order $u geq 62$ with at most $frac{u^2}{50}-frac{11u}{100}-frac{116}{75}$ triples has an embedding of order $v$ for each admissible integer $v geq frac{8u+17}{5}$." @default.
- W2952380475 created "2019-06-27" @default.
- W2952380475 creator A5028146693 @default.
- W2952380475 date "2014-02-12" @default.
- W2952380475 modified "2023-09-27" @default.
- W2952380475 title "Embedding partial Steiner triple systems with few triples" @default.
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