Removal lemmas and approximate homomorphisms
Name
removal-lemmas-and-approximate-homomorphisms.pdf
Description
Published version
Size
339.45 KB
Format
Adobe PDF
Checksum (MD5)
85fb280a15d7d6a7ccf01b173af933c2
Author(s)
Fox, Jacob
Zhao, Yufei
Date Issued
2022
Journal
Combinatorics Probability and Computing
Publisher
Cambridge University Press (CUP)
Citation
Fox, Jacob and Zhao, Yufei. 2022. "Removal lemmas and approximate homomorphisms." Combinatorics Probability and Computing, 31 (4).
Version
Final published version
Abstract
We study quantitative relationships between the triangle removal lemma and several of its variants. One such variant, which we call the triangle-free lemma, states that for each ϵ>0 there exists M such that every triangle-free graph G has an ϵ -approximate homomorphism to a triangle-free graph F on at most M vertices (here an ϵ -approximate homomorphism is a map V(G)→V(F) where all but at most ϵ|V(G)|2 edges of G are mapped to edges of F). One consequence of our results is that the least possible M in the triangle-free lemma grows faster than exponential in any polynomial in ϵ−1 . We also prove more general results for arbitrary graphs, as well as arithmetic analogues over finite fields, where the bounds are close to optimal.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1017/S0963548321000572
