Matchings in the leave of equitable partial Steiner triple systems

In this note, necessary and sufficient conditions are given for the existence of an equitable partial Steiner triple system \((S,T)\) on \(n\) symbols with exactly \(t\) triples, such that the leave of \((S,T)\) contains a \(1\)-factor if \(n\) is even and a near \(1\)-factor if \(n\) is odd.