Embedding Steiner triple systems into Steiner systems S(2,4,v)

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 Steiner triple systems into Steiner systems S(2, 4, v)

We initiate a systematic study of embeddings of Steiner triple systems into Steiner systems S(2; 4; v). We settle the existence of an embedding of the unique STS(7) and, with one possible exception, of the unique STS(9) into S(2; 4; v). We also obtain bounds for embedding sizes of Steiner triple systems of larger orders. c © 2003 Elsevier B.V. All rights reserved.

Embedding Steiner triple systems in hexagon triple systems

Bicoloring Steiner Triple Systems

A Steiner triple system has a bicoloring with m color classes if the points are partitioned into m subsets and the three points in every block are contained in exactly two of the color classes. In this paper we give necessary conditions for the existence of a bicoloring with 3 color classes and give a multiplication theorem for Steiner triple systems with 3 color classes. We also examine bicolo...

Balanced Steiner Triple Systems

A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that every pair of X is contained in exactly one triple of B. It is well known that a necessary and sufficient condition for a STS(v) to exist is that v#1 or 3 (mod 6). An r-coloring of a STS(v) is a map , : X [1, ..., r] such that at least two...