Ramsey's theorem
Hypergraphs

We can extend the definition of induced Ramsey numbers to d -uniform hypergraphs by simply changing the word graph in the statement to hypergraph. Furthermore, we can define the multicolor version of induced Ramsey numbers in the same way as the previous subsection.

Let H be a d -uniform hypergraph with k vertices. Define the tower function t (x) by letting t (x) = x and for i ≥ 1, t (x) = 2. Using the hypergraph container method, Conlon, Dellamonica, La Fleur, Rödl and Schacht were able to show that for d ≥ 3, q ≥ 2, r (H; q) ≤ t (ck) for some constant c depending on only d and q. In particular, this result mirrors the best known bound for the usual Ramsey number when d = 3.
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