TY - JOUR

T1 - The Induced Removal Lemma in Sparse Graphs

AU - Sapir, Shachar

AU - Shapira, Asaf

N1 - Publisher Copyright:
© 2019 Cambridge University Press.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The induced removal lemma of Alon, Fischer, Krivelevich and Szegedy states that if an n-vertex graph G is ϵ-far from being induced H-free then G contains δH(ϵ) · nh induced copies of H. Improving upon the original proof, Conlon and Fox proved that 1/δH(ϵ)is at most a tower of height poly(1/ϵ), and asked if this bound can be further improved to a tower of height log(1/ϵ). In this paper we obtain such a bound for graphs G of density O(ϵ). We actually prove a more general result, which, as a special case, also gives a new proof of Fox's bound for the (non-induced) removal lemma.

AB - The induced removal lemma of Alon, Fischer, Krivelevich and Szegedy states that if an n-vertex graph G is ϵ-far from being induced H-free then G contains δH(ϵ) · nh induced copies of H. Improving upon the original proof, Conlon and Fox proved that 1/δH(ϵ)is at most a tower of height poly(1/ϵ), and asked if this bound can be further improved to a tower of height log(1/ϵ). In this paper we obtain such a bound for graphs G of density O(ϵ). We actually prove a more general result, which, as a special case, also gives a new proof of Fox's bound for the (non-induced) removal lemma.

UR - http://www.scopus.com/inward/record.url?scp=85072984240&partnerID=8YFLogxK

U2 - 10.1017/S0963548319000233

DO - 10.1017/S0963548319000233

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85072984240

SN - 0963-5483

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

ER -