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.
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© 2015 Wiley Periodicals, Inc.
- Simplicial complex