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- Title
Bipodal Structure in Oversaturated Random Graphs.
- Authors
Kenyon, Richard; Radin, Charles; Ren, Kui; Sadun, Lorenzo
- Abstract
We study the asymptotics of large simple graphs directly constrained by the limiting subgraph densities of edges and 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 Erd˝ os-Rényi graph, the typical large graph is bipodal with parameters varying analytically with the densities. Asymptotically, the parameters depend only on the degree sequence of H.
- Subjects
GRAPH theory; ASYMPTOTES; GEOMETRY; ANALYTIC geometry; PARAMETER estimation
- Publication
IMRN: International Mathematics Research Notices, 2018, Vol 2018, Issue 4, p1009
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnw261