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Some results on quadrilaterals in Steiner triple systems

✍ Scribed by D.R. Stinson; Y.J. Wei

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 792 KB
Volume: 105
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90143-4

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✦ Synopsis

Stinson, D.R., Y.J. Wei, Some results on quadrilaterals in Steiner triple systems, Discrete Mathematics 105 (1992) 207-219.

In this paper, we study quadrilaterals in Steiner triple systems. We present two recursive constructions for Steiner triple systems having no quadrilaterals.

We also consider the maximum number of quadrilaterals a Steiner triple system of any given order can have. The upper bound is reached precisely when the Steiner triple system is the projective space PG(d, 2). Some recursive constructions for Steiner triple systems having 'many' quadrilaterals are also presented.

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