Partitioning Steiner triple systems into complete arcs

✍ Scribed by C.J. Colbourn; K.T. Phelps; M.J. de Resmini; A. Rosa

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 713 KB
• Volume: 89
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90363-7

✦ Synopsis

Colbourn, C.J., K.T. Phelps, M.J. de Resmini and A. Rosa, Partitioning Steiner triple systems into complete arcs, Discrete Mathematics 89 (1991) 149-160.

For a Steiner triple system of order v to have a complete s-arc one must have s(s + 1)/2 3 v with equality only if s = 1 or 2 mod 4. To partition a Steiner triple system of order s(s + 1)/2 into complete s-arcs, one must have s = 1 mod 4. In this paper we give constructions of Steiner triple systems of order s(s + 1)/2 which can be partitioned into complete s-arcs for all s = 1 mod 4. For s -1 or 5 mod 12, we construct cyclic Steiner triple systems having this property. For s -9 mod 12 we use Kirkman triple systems of order s having one additional property to construct these Steiner triple systems. We further establish that Kirkman triple systems having this additional property exist at least for s = 9 mod 24 and s -21 mod 120.