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- W2043952166 abstract "In 2009 it was established that any partial Steiner triple system of order $u$ has an embedding of order $v$ for each $vgeq 2u+1$ such that $v equiv 1,3$ (mod 6), in accordance with a conjecture of Lindner. It is known 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 $v<2u+1$, so this result is best possible in one sense. Many partial Steiner triple systems do have embeddings of orders smaller than $2u+1$, however, although little is known about when such 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.
- W2043952166 created "2016-06-24" @default.
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- W2043952166 date "2014-01-01" @default.
- W2043952166 modified "2023-09-27" @default.
- W2043952166 title "Embedding Partial Steiner Triple Systems with Few Triples" @default.
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- W2043952166 doi "https://doi.org/10.1137/130939365" @default.
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