Embeddings of a-Resolvable Steiner Triple Systems

Abstract

Let $\alpha$-resolvable STS($v$) denote a Steiner triple system of order $v$ whose blocks are partitioned into classes such that each point of the design occurs in precisely $\alpha$ blocks in each class. We show that for $v\equiv u\equiv 1(\mathrm{mod}6)$ and $v\ge 3u+4$, there exists an $\alpha$-resolvable STS($v$) containing an $\alpha$-resolvable sub-STS($u$) for all suitable $\alpha$.