给定度数的密集随机图上的循环

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-03-26 DOI:10.1016/j.jctb.2024.03.002

Lyuben Lichev , Dieter Mitsche , Guillem Perarnau

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引用次数: 0

摘要

在本文中，我们研究了具有两种随机性来源的随机图中最大连通分量的阶次：首先，从具有给定度序列的所有图中随机选择图，然后应用键渗滤。我们无法对所有此类度序列进行分类，但我们展示了最大分量阶数在两种随机性来源方面的几种新阈值现象。我们还提供了一个度序列的例子，在这个度序列中，最大分量的阶数在渗滤参数方面经历了无限制的跃迁，从而产生了一种在没有渗滤的情况下无法观察到的行为。

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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Percolation on dense random graphs with given degrees

In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied. Far from being able to classify all such degree sequences, we exhibit several new threshold phenomena for the order of the largest component in terms of both sources of randomness. We also provide an example of a degree sequence for which the order of the largest component undergoes an unbounded number of jumps in terms of the percolation parameter, giving rise to a behavior that cannot be observed without percolation.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.