随机正则图上的最大独立集

IF 4.9 1区数学 Q1 MATHEMATICS

Acta Mathematica Pub Date : 2013-10-17 DOI:10.14288/1.0044424

Jian Ding, A. Sly, Nike Sun

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引用次数: 60

摘要

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。

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Maximum independent sets on random regular graphs

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.

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来源期刊

Acta Mathematica 数学-数学

CiteScore

6.00

自引率

2.70%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes original research papers of the highest quality in all fields of mathematics.