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arXiv 0909.3271math.COmath.PR
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相依随机选择

Dependent Random Choice

Jacob Fox, Benny Sudakov

摘要:

我们描述了一个简单的,但令人惊讶的强大的概率技术,它显示了如何在一个稠密的图中找到一个大的顶点子集,其中所有(或几乎所有)的小子集有许多共同的邻居。最近,这种技术在极值图论、拉姆齐理论、加法组合学和组合几何学中有几个引人注目的应用。在本调查中,我们讨论其中的一些。

英文摘要:

We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this survey we discuss some of them.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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