Abstract
We consider a natural generalization of Turán's forbidden subgraph problem and the Ruzsa-Szemerédi problem by studying the maximum number exF(n,G) of edge-disjoint copies of a fixed graph F can be placed on an n-vertex ground set without forming a subgraph G whose edges are from different F-copies. We determine the pairs {F,G} for which the order of magnitude of exF(n,G) is quadratic and prove several asymptotic results using various tools from the regularity lemma and supersaturation to graph packing results.
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