Embedding partial triple systems (Q1112041)

The main result of this paper is that any partial triple system (S,B) of index \(\lambda\) on n points can be embedded in a triple system of any odd \(\lambda\)-admissible order greater than 4n. Furthermore, if the minimum degree, maximum degree and total number of edges in the missing-edge graph of (S,B) satisfy certain bounds, then (S,B) can be embedded in a triple system of order \(2n+1\), provided \(2n+1\) is \(\lambda\)-admissible. It is also shown that there exists an equitable partial triple system of index \(\lambda\) containing v triples of n points for any \(v\leq \mu (n,\lambda)\).