Bipodal structure in oversaturated random graphs

@article{Kenyon2015BipodalSI,
  title={Bipodal structure in oversaturated random graphs},
  author={Richard W. Kenyon and Charles Radin and Kui Ren and Lorenzo A Sadun},
  journal={ArXiv},
  year={2015},
  volume={abs/1509.05370}
}
We study the asymptotics of large simple graphs constrained by the limiting density of edges and the limiting subgraph density of an arbitrary fixed graph $H$. We prove that, for all but finitely many values of the edge density, if the density of $H$ is constrained to be slightly higher than that for the corresponding Erdős-Renyi graph, the typical large graph is bipodal with parameters varying analytically with the densities. Asymptotically, the parameters depend only on the degree sequence of… 

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