A random subgraph of a graph with minimum degree at least (1 - 1/(2Δ))n contains, with high probability, any spanning n-vertex graph of maximum degree Δ, once edges are kept with probability at least C n^{-1/m1(H)} log n.
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Robustness of the Sauer-Spencer Theorem
A random subgraph of a graph with minimum degree at least (1 - 1/(2Δ))n contains, with high probability, any spanning n-vertex graph of maximum degree Δ, once edges are kept with probability at least C n^{-1/m1(H)} log n.