2 research outputs found
Lack of Hyperbolicity in Asymptotic Erd\"os--Renyi Sparse Random Graphs
In this work we prove that the giant component of the Erd\"os--Renyi random
graph for c a constant greater than 1 (sparse regime), is not Gromov
-hyperbolic for any positive with probability tending to one
as . As a corollary we provide an alternative proof that the giant
component of when c>1 has zero spectral gap almost surely as
.Comment: Updated version with improved results and narrativ