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