Conlon, David and Fox, Jacob (2013) Graph removal lemmas. In: Surveys in Combinatorics 2013. London Mathematical Society Lecture Note Series. No.409. Cambridge University Press , Cambridge, United Kingdom, pp. 1-50. ISBN 9781139506748. https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001516
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Abstract
The graph removal lemma states that any graph on n vertices with o(n^h) copies of a fixed graph H on h vertices may be made H-free by removing o(n^2) edges. Despite its innocent appearance, this lemma and its extensions have several important consequences in number theory, discrete geometry, graph theory and computer science. In this survey we discuss these lemmas, focusing in particular on recent improvements to their quantitative aspects.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 2013 Cambridge University Press. Print publication year 2013; online publication date July 2013. Conlon supported by a Royal Society University Research Fellowship. Fox supported by a Simons Fellowship and NSF Grant DMS-1069197. The authors would like to thank Noga Alon, Zoltan Füredi, Vojta Rödl and Terry Tao for helpful comments regarding the history of the removal lemma. | |||||||||
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| Series Name: | London Mathematical Society Lecture Note Series | |||||||||
| Issue or Number: | 409 | |||||||||
| DOI: | 10.1017/cbo9781139506748.002 | |||||||||
| Record Number: | CaltechAUTHORS:20190812-163001516 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001516 | |||||||||
| Official Citation: | Conlon, David, and Jacob Fox. “Graph Removal Lemmas.” Chapter. In Surveys in Combinatorics 2013, edited by Simon R. Blackburn, Stefanie Gerke, and Mark Wildon, 1–50. London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 2013. doi:10.1017/CBO9781139506748.002. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 97850 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Melissa Ray | |||||||||
| Deposited On: | 19 Aug 2019 21:29 | |||||||||
| Last Modified: | 16 Nov 2021 17:34 |
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