For dn-regular G_d union G(n,p) with p > 2d/(1+2d), there is whp a triangle packing covering all but o(n²) edges, and the bound is sharp for d ≤ 1/2.
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Triangle packings in randomly perturbed graphs
For dn-regular G_d union G(n,p) with p > 2d/(1+2d), there is whp a triangle packing covering all but o(n²) edges, and the bound is sharp for d ≤ 1/2.