The threshold for d-collapsibility in random complexes*

Abstract

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 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. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 260–269, 2016