Fundamental Groups of Random Clique Complexes
Skip to main content
eScholarship
Open Access Publications from the University of California

Department of Mathematics

Faculty bannerUC Davis

Fundamental Groups of Random Clique Complexes

  • Author(s): Babson, Eric
  • et al.

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