Acta Mathematica

Maximum independent sets on random regular graphs

Jian Ding, Allan Sly, and Nike Sun

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Abstract

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.

Note

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1502989202

Digital Object Identifier
doi:10.1007/s11511-017-0145-9

Mathematical Reviews number (MathSciNet)
MR3689942

Zentralblatt MATH identifier
1371.05261

Rights
2016 © Institut Mittag-Leffler

Citation

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. https://projecteuclid.org/euclid.acta/1502989202


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