We prove that there exists 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. The proof is based on a carefully designed probabilistic construction and the analysis depends on entropy methods. We further extend this result to prove tight bounds on various other hypergraph Ramsey numbers.

中文翻译：

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具有禁止链接的超图中的独立集

我们证明存在一个 3-均匀超图 $N$ 具有独立数的顶点 $哦(\mathrm{日志}N/\mathrm{日志}\mathrm{日志}N)$其中任意四个顶点之间最多有两条边。这个界限是紧的，解决了拉姆齐理论中 Erdős 和 Hajnal 的一个长期悬而未决的问题。证明基于精心设计的概率构造，分析依赖于熵方法。我们进一步扩展这个结果以证明各种其他超图拉姆齐数的严格界限。