The Füredi-Frankl-Rödl theorem is a central result in extremal combinatorics that deals with the maximum number of edges in a hypergraph while avoiding certain sub-hypergraphs. Specifically, it provides bounds for the size of hypergraphs that do not contain a complete sub-hypergraph of a given size, effectively characterizing the relationship between hypergraph density and forbidden structures. This theorem has significant implications in various areas of combinatorial theory, particularly when analyzing extremal properties in hypergraphs.
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