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
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AN - SCOPUS:85072984240
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
SN - 0963-5483
ER -