English

The threshold for collapsibility in random complexes

Probability 2013-07-11 v1 Combinatorics

Abstract

In this paper we determine the threshold for collapsibility in the probabilistic model Xd(n,p)X_d(n,p) of dd-dimensional simplicial complexes. A lower bound for this threshold p=cdnp=\frac{c_d}{n} was established in \cite{ALLM}. Here we show that this is indeed the correct threshold. Namely, for every c>cdc>c_d, a complex drawn from Xd(n,cn)X_d(n,\frac{c}{n}) is asymptotically almost surely not collapsible.

Cite

@article{arxiv.1307.2684,
  title  = {The threshold for collapsibility in random complexes},
  author = {Lior Aronshtam and Nati Linial},
  journal= {arXiv preprint arXiv:1307.2684},
  year   = {2013}
}
R2 v1 2026-06-22T00:48:45.548Z