A note on the Erdős-Hajnal hypergraph Ramsey problem
A note on the Erdős-Hajnal hypergraph Ramsey problem
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关于 ErdÅs-Hajnal 超图 Ramsey 问题的注解
DOI：
10.1090/proc/15839
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发表时间：
2022
影响因子：
1
通讯作者：
Zhu, Emily
中科院分区：
文献类型：
--
作者：
Mubayi, Dhruv;Suk, Andrew;Zhu, Emily
我们证明存在一个绝对常数，使得以下内容成立。对于每一个，至少有一个具有最多独立数的顶点的5一致超图，其中每6个顶点的集合最多产生3条边。顶点数量的双指数增长率非常快。通过应用前两位作者建立的逐步引理，对于一致超图证明了类似的尖锐结果。这回答了 Erdős 和 Hajnal 于 1972 年提出的拉姆齐理论猜想的倒数第二个开放案例。
We show that there is an absolute constantsuch that the following holds. For every, there is a 5-uniform hypergraph on at leastvertices with independence number at most, where every set of 6 vertices induces at most 3 edges. The double exponential growth rate for the number of vertices is sharp. By applying a stepping-up lemma established by the first two authors, analogous sharp results are proved for-uniform hypergraphs. This answers the penultimate open case of a conjecture in Ramsey theory posed by Erdős and Hajnal in 1972. References