Embedding partial triple systems

AbstractThe main result of this paper is that any partial triple system (S, B) of index λ on n points can be embedded in a triple system of any odd λ-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 λ-admissible. It is also shown that there exists an equitable partial triple system of index λ containing ν triples on n points for any ν ⩽ μ(n, λ)