An approximate blow-up lemma for sparse pseudorandom graphs

We state a sparse approximate version of the blow-up lemma, showing that regular partitions in sufficiently pseudorandom graphs behave almost like complete partite graphs for embedding graphs with maximum degree Δ. We show that ( p , γ ) -jumbled graphs, with γ = o ( p max ( 2 Δ , Δ + 3 / 2 ) n ) , are “sufficiently pseudorandom”. proach extends to random graphs G n , p with p ≫ ( l o g n n ) 1 / Δ .