TL;DR
The paper surveys the graph removal lemma, highlighting recent quantitative improvements and its broad implications across various fields such as number theory, geometry, and computer science.
Contribution
It provides a comprehensive overview of recent advancements in the quantitative bounds of the graph removal lemma and its diverse applications.
Findings
Improved bounds on the number of edge removals needed.
Enhanced understanding of applications in multiple mathematical disciplines.
Summarization of recent research developments in the field.
Abstract
The graph removal lemma states that any graph on n vertices with o(n^{v(H)}) copies of a fixed graph H 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.
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