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arXiv · 1802.01619

Convergence of Maximum Bisection Ratio of Sparse Random Graphs

Brice Huang
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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 Erd\"os-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.

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Brice Huang. 2018-02-05. Convergence of Maximum Bisection Ratio of Sparse Random Graphs. https://doi.org/10.1214/18-ecp164

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