35 research outputs found
Bipodal structure in oversaturated random graphs
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
. We prove that, for all but finitely many values of the edge density, if
the density of is constrained to be slightly higher than that for the
corresponding Erd\H{o}s-R\'enyi graph, the typical large graph is bipodal with
parameters varying analytically with the densities. Asymptotically, the
parameters depend only on the degree sequence of