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About: Graph removal lemma     Goto   Sponge   NotDistinct   Permalink

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In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by removing a small number of edges.The special case in which the subgraph is a triangle is known as the triangle removal lemma. The graph removal lemma can be used to prove Roth's theorem on 3-term arithmetic progressions, and a generalization of it, the hypergraph removal lemma, can be used to prove Szemerédi's theorem. It also has applications to property testing.