Embeddings of Maximum Packings of Triples

Abstract

Let $\mathrm{MPT}(v,\lambda )$ denote a maximum packing of triples of order $v$ with index $\lambda$. For $\lambda >1$ and $v\ge 3$, it is proved in this paper that the necessary and sufficient condition for the embedding of an $\mathrm{MPT}(v,\lambda )$ in an $\mathrm{MPT}(u,\lambda )$ is $u\ge 20v+1$.