Maximum independent sets on random regular graphs

IF 4.9 1区 数学 Q1 MATHEMATICS
Jian Ding, A. Sly, Nike Sun
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引用次数: 60

Abstract

We determine the asymptotics of the independence number of the random d-regular graph for all $${d\geq d_0}$$d≥d0. It is highly concentrated, with constant-order fluctuations around $${n\alpha_*-c_*\log n}$$nα∗-c∗logn for explicit constants $${\alpha_*(d)}$$α∗(d) and $${c_*(d)}$$c∗(d). Our proof rigorously confirms the one-step replica symmetry breaking heuristics for this problem, and we believe the techniques will be more broadly applicable to the study of other combinatorial properties of random graphs.
随机正则图上的最大独立集
我们确定了所有$${d\geq d_0}$$ d≥d0的随机d正则图的独立数的渐近性。它是高度集中的,对于显式常数$${\alpha_*(d)}$$ α∗(d)和$${c_*(d)}$$ c∗(d),在$${n\alpha_*-c_*\log n}$$ nα∗-c∗logn附近具有常阶波动。我们的证明严格地证实了该问题的一步复制对称破断启发式,我们相信该技术将更广泛地适用于随机图的其他组合性质的研究。
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
Acta Mathematica
Acta Mathematica 数学-数学
CiteScore
6.00
自引率
2.70%
发文量
6
审稿时长
>12 weeks
期刊介绍: Publishes original research papers of the highest quality in all fields of mathematics.
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