Embeddings of almost resolvable triple systems Original Research Article

Let ARB(3,λ;v) denote an almost resolvable λ-fold system of order v. In this paper, we discuss the embedding problem for almost resolvable triple systems and prove that for any λ (λ≡0 (mod 2)), the necessary and sufficient conditions for the embedding of an ARB(3,λ;v) in an ARB(3,λ;u) are u⩾3v+1 and u≡v≡1 (mod 3).