Maximum independent sets on random regular graphs

Jian Ding; Allan Sly; Nike Sun

doi:10.1007/s11511-017-0145-9

Maximum independent sets on random regular graphs

Jian Ding
, Allan Sly
, Nike Sun

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

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_∗log n 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.

Original language	English (US)
Pages (from-to)	263-340
Number of pages	78
Journal	Acta Mathematica
Volume	217
Issue number	2
DOIs	https://doi.org/10.1007/s11511-017-0145-9
State	Published - Dec 1 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11511-017-0145-9

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title = "Maximum independent sets on random regular graphs",

abstract = "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∗log n 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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AU - Sun, Nike

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AB - 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∗log n 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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Maximum independent sets on random regular graphs

Abstract

All Science Journal Classification (ASJC) codes

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