An approximate blow-up lemma for sparse pseudorandom graphs

Peter Allen, Julia Böttcher, Hiệp Hàn, Yoshiharu Kohayakawa, Yury Person
2013 Electronic Notes in Discrete Mathematics  
We state a sparse approximate version of the blow-up lemma, showing that regular partitions in su ciently pseudorandom graphs behave almost like complete partite graphs for embedding graphs with maximum degree . We show that (p, )-jumbled graphs, with = o(p max(2 , +3/2) n), are "su ciently pseudorandom". The approach extends to random graphs G n,p with p log n n 1/ .
doi:10.1016/j.endm.2013.10.061 fatcat:unehq3cnibfkva4s5q5tfit7xy