Constructions in Ramsey theory
Constructions in Ramsey theory
复制标题
拉姆齐理论的构建
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Andrew Suk
中科院分区：
文献类型：
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作者：
D. Mubayi;Andrew Suk
我们为拉姆西理论提供了几种构造，我们证明了经典的4-均匀的拉姆西号R4（5，n）的超质量下限 - 均匀版本RK（K+1，n）。由于作者的第二，我们证明了HypergraphErdős -Rogers功能FK+1，K+2K（n）的上限（k -13） - 折。这只是对数，并解决了Dudek的问题，而Conlon，Fox和Sudakov重申的第一作者都将Erdős和Hajnal的结果概括为3均匀的Ramsey的结果K-均匀的超图。
We provide several constructions for problems in Ramsey theory. First, we prove a superexponential lower bound for the classical 4‐uniform Ramsey number r4(5,n) , and the same for the iterated (k−4) ‐fold logarithm of the k ‐uniform version rk(k+1,n) . This is the first improvement of the original exponential lower bound for r4(5,n) implicit in work of Erdős and Hajnal from 1972 and also improves the current best known bounds for larger k due to the authors. Second, we prove an upper bound for the hypergraph Erdős–Rogers function fk+1,k+2k(N) that is an iterated (k−13) ‐fold logarithm in N . 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 of K4 minus an edge versus a clique to k ‐uniform hypergraphs.
影响因子：
4.9
作者：
Chattopadhyay, Eshan;Zuckerman, David
通讯作者：
Zuckerman, David