le of an edge-coloured graph \(G^*\) such that there is no finite integer \(n\) for which it is possible to decompose \(rK_n^*\) into edge-disjoint colour-identical copies of \(G^*\). We investigate the problem of determining precisely when an edge-coloured graph \(G^*\) with \(r\) colours admits a \(G^*\)-decomposition of \(rK_n^*\), for some finite \(n\). We also investigate conditions under which any partial edge-coloured \(G^*\)-decomposition of \(rK_n^*\) has a finite embedding.
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