Existence of incomplete resolvable minimum coverings of pairs by triples Original Research Article

For given positive integers u and v with u≡v≡0 (mod 6), let IRC(u,v) denote an incomplete resolvable minimum covering of pairs by triples of order u having a hole of size v. It is proved in this paper that there exists such an IRC(u,v) if and only if u⩾3v.