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2018 Convergence of maximum bisection ratio of sparse random graphs
Brice Huang
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP164

Abstract

We consider sequences of large sparse random graphs whose degree distribution approaches a limit with finite mean. This model includes both the random regular graphs and the Erdös-Renyi graphs of constant average degree. We prove that the maximum bisection ratio of such a graph sequence converges almost surely to a deterministic limit. We extend this result to so-called 2-spin spin glasses in the paramagnetic to ferromagnetic regime. Our work generalizes the graph interpolation method to some non-additive graph parameters.

Citation

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Brice Huang. "Convergence of maximum bisection ratio of sparse random graphs." Electron. Commun. Probab. 23 1 - 10, 2018. https://doi.org/10.1214/18-ECP164

Information

Received: 28 February 2018; Accepted: 16 August 2018; Published: 2018
First available in Project Euclid: 1 September 2018

zbMATH: 1398.05182
MathSciNet: MR3852265
Digital Object Identifier: 10.1214/18-ECP164

Subjects:
Primary: 05C80, 60C05
Secondary: 82-08

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