Maximum independent sets on random regular graphs

Jian Ding University of Chicago Allan Sly University of California, Berkeley Nike Sun Stanford University

Probability mathscidoc:1911.43040

Gold Award Paper in 2020

Acta Mathematica, 217, (2), 263-340, 2016
We determine the asymptotics of the independence number of the random d-regular graph for all d≥d0. It is highly concentrated, with constant-order fluctuations around nα∗−c∗logn 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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  title={Maximum independent sets on random regular graphs},
  author={Jian Ding, Allan Sly, and Nike Sun},
  booktitle={Acta Mathematica},
Jian Ding, Allan Sly, and Nike Sun. Maximum independent sets on random regular graphs. 2016. Vol. 217. In Acta Mathematica. pp.263-340.
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