The Induced Removal Lemma in Sparse Graphs

Shachar Sapir, Asaf Shapira*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
JournalCombinatorics Probability and Computing
StatePublished - 1 Jan 2019


FundersFunder number
Horizon 2020 Framework Programme633509


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