Open Access
2016 Maximum independent sets on random regular graphs
Jian Ding, Allan Sly, Nike Sun
Author Affiliations +
Acta Math. 217(2): 263-340 (2016). DOI: 10.1007/s11511-017-0145-9


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.

Funding Statement

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


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Jian Ding. Allan Sly. Nike Sun. "Maximum independent sets on random regular graphs." Acta Math. 217 (2) 263 - 340, 2016.


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

zbMATH: 1371.05261
MathSciNet: MR3689942
Digital Object Identifier: 10.1007/s11511-017-0145-9

Rights: 2016 © Institut Mittag-Leffler

Vol.217 • No. 2 • 2016
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