Abstract Let G be a graph whose edges are colored with k colors, and H=(H1,⋯,Hk) be a k‐tuple of graphs. 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 copy of Hi in color i, for some 1≤i≤k. Let φk(n,H) be the smallest number ϕ, such that, for every order‐n graph and every k‐edge‐coloring, there is a monochromatic H‐decomposition with at most ϕ elements. Extending the previous results of Liu and Sousa [Monochromatic Kr‐decompositions of graphs, J Graph Theory 76 (2014), 89–100], we solve this problem when each graph in H is a clique and n≥n0(H) is sufficiently large.

中文翻译：

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图的单色团分解

摘要 设 G 为边用 k 种颜色着色的图，H=(H1,⋯,Hk) 为图的 ak 元组。G 的单色 H 分解是 G 的边集的一个分区，使得每个部分要么是单个边，要么形成颜色为 i 的 Hi 的单色副本，对于某些 1≤i≤k。令 φk(n,H) 是最小的数 φ，这样，对于每个 n 阶图和每个 k 边着色，都有一个至多 φ 元素的单色 H 分解。扩展 Liu 和 Sousa 之前的结果 [Monochromatic Kr-decompositions of graphs, J Graph Theory 76 (2014), 89-100]，当 H 中的每个图都是一个团并且 n≥n0(H) 足够时，我们解决了这个问题大。