Convergence of Maximum Bisection Ratio of Sparse Random Graphs
Probability
2018-09-05 v2
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.
Cite
@article{arxiv.1802.01619,
title = {Convergence of Maximum Bisection Ratio of Sparse Random Graphs},
author = {Brice Huang},
journal= {arXiv preprint arXiv:1802.01619},
year = {2018}
}
Comments
11 pages, 1 figure; added acknowledgement of a previous unpublished result