Embedding partial triple systems

Embedding Partial Steiner Triple Systems

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 Stei...

The embedding of partial triple systems when 4 divides lambda

We show that if 4 divides I, then any partial triple system of order r and index 1 can be embedded in a proper triple system of index I and order n whenever n is I-admissible and n > 2r + 1. Moreover we find a set of necessary conditions for the embedding of a partial triple system of index I when I is even and show that when 4 divides 1, then a very closely related set of conditions is suffici...

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.

The embedding problem for partial Steiner triple systems

The system has the nice property that any pair of distinct elements of V occurs in exactly one of the subsets. This makes it an example of a Steiner triple system. Steiner triple systems first appeared in the mathematical literature in the mid-nineteenth century but the concept must surely have been thought of long before then. An excellent historical introduction appears in [7]. As pointed out...

Embedding Steiner triple systems in hexagon triple systems