Abstract
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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