Embeddings of a-Resolvable Steiner Triple Systems

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 \(v \equiv u \equiv 1 \pmod{6}\) and \(v \geq 3u + 4\), there exists an \(\alpha\)-resolvable STS(\(v\)) containing an \(\alpha\)-resolvable sub-STS(\(u\)) for all suitable \(\alpha\).