A new proof of the graph removal lemma
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Fox_A New.pdf
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143.41 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Fox, Jacob
Date Issued
April 2012
Journal
Annals of Mathematics
Publisher
Annals of Mathematics, Princeton University
Citation
Fox, Jacob. “A New Proof of the Graph Removal Lemma.” Annals of Mathematics 174.1 (2011): 561–579. Web. 20 Apr. 2012. © 2012 Annals of Mathematics
Version
Author's final manuscript
Abstract
Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n[superscript h]) copies of H can be made H-free by removing o(n[superscript 2]) edges. We give a new proof which avoids Szemerédi’s regularity lemma and gives a better bound. This approach also works to give improved bounds for the directed and multicolored analogues of the graph removal lemma. This answers questions of Alon and Gowers.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.4007/annals.2011.174.1.17
