More on decompositions of edge-colored complete graphs

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^((r))_n 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^((r))_n, each of which is an isomorphic copy of some graph in g, so that each edge of K^((r))_n appears in exactly one of the subgraphs in D.