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arXiv · 1006.1300

A new proof of the graph removal lemma

Jacob Fox
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Abstract

Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n^h) copies of H can be made H-free by removing o(n^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.

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Jacob Fox. 2010-12-31. A new proof of the graph removal lemma. https://arxiv.org/abs/1006.1300

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