Fundamental Groups of Random Clique Complexes
Open Access Publications from the University of California

## Published Web Location

https://arxiv.org/pdf/1207.5028.pdf
No data is associated with this publication.
Abstract

Clique complexes of Erd\H{o}s-R {e}nyi random graphs with edge probability between $n^{-{1\over 3}}$ and $n^{-{1\over 2}}$ are shown to be aas not simply connected. This entails showing that a connected two dimensional simplicial complex for which every subcomplex has fewer than three times as many edges as vertices must have the homotopy type of a wedge of circles, two spheres and real projective planes. Note that $n^{-{1\over 3}}$ is a threshold for simple connectivity and $n^{-{1\over 2}}$ is one for vanishing first $\F_2$ homology.

Item not freely available? Link broken?
Report a problem accessing this item