The saturation number is a concept in combinatorics that quantifies the minimum number of edges required in a graph or hypergraph before a specified substructure cannot be avoided, even if more edges are added. It connects closely to the idea of extremal graph theory, where one seeks to determine how large a structure can be without containing certain substructures. This number highlights the balance between the addition of edges and the emergence of these substructures, making it crucial for understanding Turán-type problems and saturation problems.
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