随机图中对称扩展的最大数量

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-09-16 DOI:10.1137/23m1588706

Stepan Vakhrushev, Maksim Zhukovskii

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引用次数: 0

摘要

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2468-2488 页，2024 年 9 月。摘要众所周知，经过适当的重定标后，二叉随机图的最大度在分布上收敛于 Gumbel 随机变量。对于[math]顶点集的最大公共邻接数和共享单个顶点的最大[math]小群数来说也是如此。这些结果能否推广到[数学]顶点集合的最大扩展数，即[数学]顶点集合以任何给定的方式扩展一个[数学]顶点集合？在本文中，我们将上述结果推广到一类 "对称扩展"，并证明其极限分布不一定来自 Gumbel 族。

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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Maximum Number of Symmetric Extensions in Random Graphs

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2468-2488, September 2024.
Abstract. It is known that after an appropriate rescaling the maximum degree of the binomial random graph converges in distribution to a Gumbel random variable. The same holds true for the maximum number of common neighbors of a [math]-vertex set and for the maximum number of [math]-cliques sharing a single vertex. Can these results be generalized to the maximum number of extensions of a [math]-vertex set for any given way of extending a [math]-vertex set by an [math]-vertex set? In this paper, we generalize the abovementioned results to a class of “symmetric extensions” and show that the limit distribution is not necessarily from the Gumbel family.

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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.