# 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…

## 22 Citations

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