Monochromatic K r ‐Decompositions of Graphs

Given graphs G and H , and a coloring of the edges of G with k colors, a monochromatic H‐decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic graph isomorphic to H . Letϕ k ( n , H )be the smallest number ϕ such that any graph G of order n and any coloring of its edges with k colors, admits a monochromatic H ‐decomposition with at most ϕ parts. Here, we study the functionϕ k ( n , K r )for k ≥ 2 and r ≥ 3 .