Symmetric Hypergraph Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Symmetric hypergraph theorem is a theorem in combinatorics that puts an upper bound on the chromatic number of a graph (or hypergraph in general). The original reference for this paper is unknown at the moment, and has been called folklore.A group G acting on a set S is called transitive if given any two elements x and y in S, there exists an element f of G such that f(x) = y. A graph (or hypergraph) is called symmetric if it''s automorphism group is transitive.Th...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Symmetric hypergraph theorem is a theorem in combinatorics that puts an upper bound on the chromatic number of a graph (or hypergraph in general). The original reference for this paper is unknown at the moment, and has been called folklore.A group G acting on a set S is called transitive if given any two elements x and y in S, there exists an element f of G such that f(x) = y. A graph (or hypergraph) is called symmetric if it''s automorphism group is transitive.This theorem has applications to Ramsey theory, specifically graph Ramsey theory. Using this theorem, a relationship between the graph Ramsey numbers and the extremal numbers can be shown (see Graham-Rothschild-Spencer for the details).
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