An approximate blow-up lemma for sparse pseudorandom graphs

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Abstract

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(pmax(2Δ,Δ+3/2)n), are “sufficiently pseudorandom”.

The approach extends to random graphs Gn,p with p(lognn)1/Δ.

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Partially supported by NUMEC/USP (Project MaCLinC/USP).

1

Supported by FAPESP (Proc. 2010/16526-3).

2

Partially supported by CNPq (308509/2007-2, 484154/2010-9).

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