A Simple Path to Component Sizes in Critical Random Graphs

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-05-07 DOI:10.1137/22m151056x

Umberto De Ambroggio

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1492-1525, June 2024.
Abstract. We describe a robust methodology, based on the martingale argument of Nachmias and Peres and random walk estimates, to obtain simple upper and lower bounds on the size of a maximal component in several random graphs at criticality. Even though the main result is not new, we believe the material presented here is interesting because it unifies several proofs found in the literature into a common framework. More specifically, we give easy-to-check conditions that, when satisfied, allow an immediate derivation of the above-mentioned bounds.

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临界随机图中组件大小的简单路径

SIAM 离散数学杂志》第 38 卷第 2 期第 1492-1525 页，2024 年 6 月。摘要。我们描述了一种基于 Nachmias 和 Peres 的马丁格尔论证以及随机漫步估计的稳健方法，以获得临界时几个随机图中最大分量大小的简单上界和下界。尽管主要结果并不是新的，但我们认为这里介绍的材料很有趣，因为它将文献中的几个证明统一到了一个共同的框架中。更具体地说，我们给出了易于检查的条件，这些条件一旦满足，就可以立即推导出上述边界。

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.