Some Cubic Time Regularity Algorithms for Triple Systems

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-02-05 DOI:10.1137/21m145046x

Brendan Nagle, John Theado

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 668-701, March 2024.
Abstract. Szemerédi’s regularity lemma guarantees that, for fixed [math], every graph [math] admits an [math]-regular and [math]-equitable partition [math], where [math]. These partitions are constructed by Kohayakawa, Rödl, and Thoma in time [math]. Analogous partitions of [math]-graphs [math] are constructed by Czygrinow and Rödl in time [math]. For [math], we construct these partitions (and others with slightly stronger regularity) in time [math]. We also discuss some applications.

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三重系统的一些立方时间正则算法

SIAM 离散数学杂志》，第 38 卷第 1 期，第 668-701 页，2024 年 3 月。摘要。Szemerédi 的正则性 Lemma 保证，对于固定的 [math]，每个图 [math] 都有一个 [math] 正则且 [math] 公平的分割 [math]，其中 [math]。这些分区由小早川、罗德尔和索马在[math]时间内构造。类似的[math]图[math]分区是由 Czygrinow 和 Rödl 在[math]时间内构造的。对于[math]，我们在[math]时间内构造了这些分区（以及其他规律性稍强的分区）。我们还讨论了一些应用。

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

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.