Steiner triple systems with disjoint or intersecting subsystems

Charles J. Colbourn; Monica A. Oravas; Rolf S. Rees

doi:10.1002/(SICI)1520-6610(2000)8:1<58::AID-JCD8>3.0.CO;2-2

Steiner triple systems with disjoint or intersecting subsystems

Charles J. Colbourn, Monica A. Oravas, Rolf S. Rees

Research output: Contribution to journal › Article

5 Scopus citations

Abstract

The existence of incomplete Steiner triple systems of order v having holes of orders w and u meeting in z elements is examined, with emphasis on the disjoint (z = 0) and intersecting (z = 1) cases. When w ≥ u and v = 2w + u - 2z, the elementary necessary conditions are shown to be sufficient for all values of z. Then for z ∈ {0, 1} and v "near" the minimum of 2w + u - 2z, the conditions are again shown to be sufficient. Consequences for larger orders are also discussed, in particular the proof that when one hole is at least three times as large as the other, the conditions are again sufficient.

Original language	English (US)
Pages (from-to)	58-77
Number of pages	20
Journal	Journal of Combinatorial Designs
Volume	8
Issue number	1
DOIs	https://doi.org/10.1002/(SICI)1520-6610(2000)8:1<58::AID-JCD8>3.0.CO;2-2
State	Published - Jan 1 2000
Externally published	Yes

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Keywords

Incomplete pairwise balanced design
Steiner triple system

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

Colbourn, C. J., Oravas, M. A., & Rees, R. S. (2000). Steiner triple systems with disjoint or intersecting subsystems. Journal of Combinatorial Designs, 8(1), 58-77. https://doi.org/10.1002/(SICI)1520-6610(2000)8:1<58::AID-JCD8>3.0.CO;2-2

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10.1002/(SICI)1520-6610(2000)8:1<58::AID-JCD8>3.0.CO;2-2