Embedding Partial Steiner Triple Systems
نویسنده
چکیده
We prove that a partial Steiner triple system 8 of order n can be embedded in a Steiner triple system T of any given admissible order greater than 4w. Furthermore, if G(S), the missing-edge graph of S, has the property that A(G)<ri(n + l)l and \E(G)\ then # can be embedded in a Steiner triple system of order 2n +1, provided that 2w +1 is admissible. We also prove that if there is a partial Steiner triple system of order n with v triples then there is an equitable partial Steiner triple system of order n with v triples. This result, interesting in itself, is used in the proof of the above theorems.
منابع مشابه
Embedding partial Steiner triple systems so that their automorphisms extend
It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on v points, in such a way that all automorphisms of U can be extended to V , for every admissible v satisfying v > g(u). We find exponential upper and lower bounds for g.
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