Acta Mathematica

Maximum independent sets on random regular graphs

Jian Ding, Allan Sly, and Nike Sun

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We determine the asymptotics of the independence number of the random d-regular graph for all dd0. It is highly concentrated, with constant-order fluctuations around nα-clogn 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.


Research supported by NSF grant DMS-1313596 (J. D.), Sloan Research Fellowship (A. S.), NDSEG and NSF GRF (N. S.).

Article information

Acta Math., Volume 217, Number 2 (2016), 263-340.

Received: 23 March 2014
Revised: 11 January 2016
First available in Project Euclid: 17 August 2017

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2016 © Institut Mittag-Leffler


Ding, Jian; Sly, Allan; Sun, Nike. Maximum independent sets on random regular graphs. Acta Math. 217 (2016), no. 2, 263--340. doi:10.1007/s11511-017-0145-9.

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