We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6-sparse systems for an infinite set of orders. Observations are also made concerning existing construction… (More)
This is a preprint of an article accepted for publication in Discrete Mathematics c 2002 (copyright owner as specified in the journal). Abstract A Steiner triple system, STS(v), is said to be χ-chromatic if the points can be coloured using χ colours, but no fewer, such that no block is monochromatic. All known 3-chromatic STS(v) are also equitably… (More)
Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5-sparse, but no 6-sparse, STS(19); there is exactly one uniform STS(19); there are exactly two STS(19) with no almost parallel classes; all STS(19) have chromatic number 3; all have chromatic index 10, except for 4 075 designs with… (More)
We investigate the conditions under which a Steiner triple system can have a 2-or 3-existentially closed block intersection graph.
We give a construction that produces 6-sparse Steiner triple systems of order v for all sufficiently large v of the form 3p, p prime and p ≡ 3 (mod 4). We also give a complete list of all 429 6-sparse systems with v < 10000 produced by this construction.
This is a preprint of an article accepted for publication in Ars Combi-natoria c 2004 (copyright owner as specified in the journal). Abstract A set of points in a Steiner triple system (STS(v)) is said to be independent if no three of these points occur in the same block. In this paper we derive for each k ≤ 8 a closed formula for the number of independent… (More)