The threshold for d-collapsibility in random complexes

L. Aronshtam*, N. Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


In this paper we determine the threshold for d-collapsibility in the probabilistic model Xd(n,p) of d-dimensional simplicial complexes. A lower bound for this threshold p=ηdn was established in (Aronshtam and Linial, Random Struct. Algorithms 46 (2015) 26-35), and here we show that this is indeed the correct threshold. Namely, for every c>ηd, a complex drawn from is asymptotically almost surely not d-collapsible.

Original languageAmerican English
Pages (from-to)260-269
Number of pages10
JournalRandom Structures and Algorithms
Issue number2
StatePublished - 1 Mar 2016

Bibliographical note

Publisher Copyright:
© 2015 Wiley Periodicals, Inc.


  • Collapsibility
  • Combinatory
  • Simplicial complex
  • Topology


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