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In this paper we continue the study of a natural generalisation of Tur\'an'sforbidden subgraph problem and the Ruzsa-Szemer\'edi problem. Let $ex_F(n,G)$denote the maximum number of edge-disjoint copies of a fixed simple graph $F$that can be placed on an $n$-vertex ground set without forming a subgraph $G$whose edges are from different $F$-copies. The case when both $F$ and $G$ aretriangles essentially gives back the theorem of Ruzsa and Szemer\'edi, and weextend their results for the case of arbitrary pairs of cliques by applying anumber theoretic result due to Alon and Shapira. We also settle the case when$F$ is a pentagon and $G$ is a triangle and give bounds for longer cycles aswell.

Multicolor Tur\'an numbers II. -- a generalization of the Ruzsa-Szemer\'edi theorem and new results on cliques and odd cycles