Ramsey Theory is a branch of mathematics and combinatorial theory that studies conditions under which a certain structure must appear within a larger set. It fundamentally asserts that in any sufficiently large structure, patterns or order must emerge, regardless of how the elements are arranged. This concept is closely related to Turán's theorem, which deals with the maximum number of edges in graphs that do not contain a complete subgraph of a certain size, showcasing the interplay between extremal graph properties and Ramsey-type results.
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