Let be a graph of size with vertex set and edge set . A -\emph{labeling} of is a one-to-one function such that , where for each either or . Such a labeling of yields a cyclic -decomposition of . It is conjectured by El-Zanati and Vanden Eynden that every 2-regular graph admits a -labeling. We show that the union of up to ten vertex-disjoint admits a -labeling.