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Linear Ramsey numbers for bounded-degree hypergraphs

Yoshiyasu Ishigami
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Abstract

We show that the Ramsey number is linear for every uniform hypergraph with bounded-degree. This is a hypergraph extension of the famous theorem for ordinary graphs which Chvátal et al. showed in 1983. Our proof is simple, contains the multicolor case, and provides a strong embedding lemma. It shows the potential of a new hypergraph regularity lemma by the author.

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Yoshiyasu Ishigami. 2007-12-13. Linear Ramsey numbers for bounded-degree hypergraphs. https://arxiv.org/abs/math/0612601

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