Embedding spanning bounded degree subgraphs in randomly perturbed graphs

We study the model of randomly perturbed dense graphs, which is the union of any graph Gα with minimum degree αn and the binomial random graph G(n,p). For p=ω(n−2/(Δ+1)), we show that Gα∪G(n,p) contains any single spanning graph with maximum degree Δ. As in previous results concerning this model, the bound for p we use is lower by a log-term in comparison to the bound known to be needed to find the same subgraph in G(n,p) alone.