Partitioning Steiner triple systems into complete arcs

Charles Colbourn, K. T. Phelps, M. J. de Resmini, A. Rosa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

For a Steiner triple system of order v to have a complete s-arc one must have s(s + 1)/2≥v with equality only if s = 1 or 2 mod 4. To partition a Steiner triplesystem of order s(s + 1) 2 into complete s-arcs, one must have s = 1 mod 4. In this paper wegive 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.

Original languageEnglish (US)
Pages (from-to)149-160
Number of pages12
JournalDiscrete Mathematics
Volume89
Issue number2
DOIs
StatePublished - May 15 1991
Externally publishedYes

Fingerprint

Steiner Triple System
Partitioning
Arc of a curve
Triple System
Equality
Partition

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Partitioning Steiner triple systems into complete arcs. / Colbourn, Charles; Phelps, K. T.; de Resmini, M. J.; Rosa, A.

In: Discrete Mathematics, Vol. 89, No. 2, 15.05.1991, p. 149-160.

Research output: Contribution to journalArticle

Colbourn, Charles ; Phelps, K. T. ; de Resmini, M. J. ; Rosa, A. / Partitioning Steiner triple systems into complete arcs. In: Discrete Mathematics. 1991 ; Vol. 89, No. 2. pp. 149-160.
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