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arXiv · 1206.4257

Three Proofs of the Hypergraph Ramsey Theorem (An exposition)

William Gasarch·Andy Parrish·Sandow Sinai
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Abstract

Ramsey, Erdos-Rado, and Conlon-Fox-Sudakov have given proofs of the 3-hypergraph Ramsey Theorem with better and better upper bounds on the 3-hypergraph Ramsey Number. Ramsey and Erdos-Rado also prove the a-hypergraph Ramsey Theorem. Conlon-Fox-Sudakov note that their upper bounds on the 3-hypergraph Ramsey Numbers, together with a recurrence of Erdos-Rado (which was the key to the Erdos-Rado proof), yield improved bounds on the a-hypergraph Ramsey numbers. We present all of these proofs and state explicit bounds for the 2-color case and the c-color case. We give a more detailed analysis of the construction of Conlon-Fox-Sudakov and hence obtain a slightly better bound.

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William Gasarch, Andy Parrish, Sandow Sinai. 2012-06-19. Three Proofs of the Hypergraph Ramsey Theorem (An exposition). https://arxiv.org/abs/1206.4257

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