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

@article{Benini2010DownlinkingT, title={Down-linking \$(K\_v,\Gamma)\$-designs to \$P\_3\$-designs}, author={Anna Benini and Luca Giuzzi and Anita Pasotti}, journal={arXiv: Combinatorics}, year={2010} }

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 of B into one of its subgraphs. This is a new concept, closely related with both the notion of metamorphosis and that of embedding. In the present paper we study down-links in general and prove that any (K_v,G)-design might be down-linked to a (K_n,G')-design, provided that n is admissible and large enough. We also show that if G'=P_3, it is always possible…

## One Citation

### New results on path-decompositions and their down-links

- Computer Science
- 2011

The spectrum problems for œ = P4 are studied and general results on the existence of path-decompositions and embeddings between pathdecomposition playing a fundamental role for the construction of down-links are presented.

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