Unbalanced steiner 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...

5-Chromatic Steiner Triple Systems

We show that, up to an automorphism, there is a unique independent set in PG(5,2) that meet every hyperplane in 4 points or more. Using this result, we show that PG(5,2) is a 5-chromatic STS. Moreover, we construct a 5-chromatic STS(v) for every admissible v ≥ 127.

Linearly Derived Steiner 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...