Constructions in Ramsey theory: CONSTRUCTIONS IN RAMSEY THEORY
Constructions in Ramsey theory: CONSTRUCTIONS IN RAMSEY THEORY
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拉姆齐理论的构造：拉姆齐理论的构造
DOI：
10.1112/jlms.12102
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Suk, Andrew
中科院分区：
文献类型：
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作者：
Mubayi, Dhruv;Suk, Andrew
我们为Ramsey理论中的问题提供了几个构造性。首先，我们证明了经典的4-一致Ramsey数的一个超指数下界，以及-一致形式的重对数的一个超指数下界。这是自1972年Erd、ő、S和Hajal工作以来对原隐式的指数下界的首次改进，也改进了目前已知的更大的下界。其次，我们证明了超图ERD-őS-罗杰斯函数的一个上界，即文[1]中的重对数。这改进了以前只是对数的上界，并解决了杜德克和第一作者的问题，康伦、福克斯和苏达科夫重申了这个问题。第三，我们推广了Erd，ő，S和Hajnal关于减边相对于团到一致超图的3一致Ramsey数的结果。
We provide several constructions for problems in Ramsey theory. First, we prove a superexponential lower bound for the classical 4‐uniform Ramsey number, and the same for the iterated‐fold logarithm of the‐uniform version. This is the first improvement of the original exponential lower bound forimplicit in work of Erdős and Hajnal from 1972 and also improves the current best known bounds for largerdue to the authors. Second, we prove an upper bound for the hypergraph Erdős–Rogers functionthat is an iterated‐fold logarithm in. This improves the previous upper bounds that were only logarithmic and addresses a question of Dudek and the first author that was reiterated by Conlon, Fox and Sudakov. Third, we generalize the results of Erdős and Hajnal about the 3‐uniform Ramsey number ofminus an edge versus a clique to‐uniform hypergraphs.