In a recent paper the concept of \emph{down-link} from a $(K_v,\Gamma)$-design $\cB$ to a $(K_n,\Gamma')$-design $\cB'$ has been introduced. In the present paper the spectrum problems for $\Gamma'=P_4$ are studied. General results on the existence of path-decompositions and embeddings between path-decompositions playing a fundamental role for the construction of down-links are also presented.

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

#### Abstract

In a recent paper the concept of \emph{down-link} from a $(K_v,\Gamma)$-design $\cB$ to a $(K_n,\Gamma')$-design $\cB'$ has been introduced. In the present paper the spectrum problems for $\Gamma'=P_4$ are studied. General results on the existence of path-decompositions and embeddings between path-decompositions playing a fundamental role for the construction of down-links are also presented.
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2013
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/87904