Abstract
Let G be a family of graphs whose edges are colored with elements from a set R of r colors. We assume no two vertices of G are joined by more than one edge of color i for any i ∈ R , for each G ∈ G . K n ( r ) will denote the complete graph with r edges joining any pair of distinct vertices, one of each of the r colors. We describe necessary and asymptotically sufficient conditions on n for the existence of a family D of subgraphs of K n ( r ) , each of which is an isomorphic copy of some graph in G , so that each edge of K n ( r ) appears in exactly one of the subgraphs in D .
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