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Let G' be a subgraph of a graph G. We define a down-link from a(K_v,G)-design B to a (K_n,G')-design B' as a map f:B->B' mapping any block ofB into one of its subgraphs. This is a new concept, closely related with boththe notion of metamorphosis and that of embedding. In the present paper westudy down-links in general and prove that any (K_v,G)-design might bedown-linked to a (K_n,G')-design, provided that n is admissible and largeenough. We also show that if G'=P_3, it is always possible to find a down-linkto a design of order at most v+3. This bound is then improved for severalclasses of graphs Gamma, by providing explicit constructions.

Down-linking $(K_v,\Gamma)$-designs to $P_3$-designs