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arXiv · 1310.4787

Maximum independent sets on random regular graphs

Jian Ding·Allan Sly·Nike Sun
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Abstract

We determine the asymptotics of the independence number of the random $d$-regular graph for all $d \ge d_0$. It is highly concentrated, with constant-order fluctuations around $nα_* - c_*\log n$ for explicit constants $α_*(d)$ and $c_*(d)$. 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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Jian Ding, Allan Sly, Nike Sun. 2013-10-17. Maximum independent sets on random regular graphs. https://arxiv.org/abs/1310.4787

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