Matchings in the Leave of Equitable Partial Steiner Triple Systems

Abstract

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.