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arXiv · 1909.05988

Independent sets in hypergraphs with a forbidden link

Jacob Fox·Xiaoyu He
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Abstract

We give a probabilistic construction of a $3$-uniform hypergraph on $N$ vertices with independence number $O(\log N / \log \log N)$ in which there are at most two edges among any four vertices. This bound is tight and solves a longstanding open problem of Erdős and Hajnal in Ramsey theory. We further extend this result to prove tight bounds on various other hypergraph Ramsey numbers.

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Jacob Fox, Xiaoyu He. 2021-03-18. Independent sets in hypergraphs with a forbidden link. https://doi.org/10.1112/plms.12400

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