Embedding partial steiner triple systems is NP-complete

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...

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

Complete Arcs in Steiner Triple Systems

A complete arc in a design is a set of elements which contains no block, and is maximal with respect to this property. The spectrum of sizes of complete arcs in Steiner triple systems is determined without exception here.