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

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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@inproceedings{jian2016maximum,
  title={Maximum independent sets on random regular graphs},
  author={Jian Ding, Allan Sly, and Nike Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128152524825749551},
  booktitle={Acta Mathematica},
  volume={217},
  number={2},
  pages={263-340},
  year={2016},
}
Jian Ding, Allan Sly, and Nike Sun. Maximum independent sets on random regular graphs. 2016. Vol. 217. In Acta Mathematica. pp.263-340. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128152524825749551.
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