On The Existence And Embedding Of Edge-Coloured Graph Decompositions

Abstract

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