  We prove the existence of infinite classes of cyclic G-decompositions of the
complete multipartite graph, G being a caterpillar, a hairy cycle or a cycle.
All the results are obtained by the construction of d-divisible
$\alpha$-labelings of G, introduced in [A. Pasotti, On d-graceful labelings, to
appear on Ars Combin.] as a generalization of classical $\alpha$-labelings,
whose existence implies that one of graph decompositions.
