Hypergraph regularity and random sampling

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2021-10-04 DOI:10.1002/rsa.21126

Felix Joos, Jaehoon Kim, Daniela Kühn, Deryk Osthus

引用次数: 0

Abstract

Suppose that a k ‐uniform hypergraph H satisfies a certain regularity instance (that is, there is a partition of H given by the hypergraph regularity lemma into a bounded number of quasirandom subhypergraphs of prescribed densities). We prove that with high probability a large enough uniform random sample of the vertex set of H also admits the same regularity instance. Here the crucial feature is that the error term measuring the quasirandomness of the subhypergraphs requires only an arbitrarily small additive correction. This has applications to combinatorial property testing. The graph case of the sampling result was proved by Alon, Fischer, Newman and Shapira.

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超图正则性与随机抽样

假设一个k‐一致超图H满足一定的正则性实例(即，存在一个由超图正则引理给出的H分割成有限数量的规定密度的准随机子超图)。我们以高概率证明了H的顶点集的一个足够大的均匀随机样本也存在相同的正则性实例。这里的关键特征是测量子超图的准随机性的误差项只需要任意小的加性校正。这也适用于组合性能测试。Alon, Fischer, Newman和Shapira证明了采样结果的图格。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.