The threshold for d-collapsibility in random complexes
نویسندگان
چکیده
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 = ηd n was established in [?], and here we show that this is indeed the correct threshold. Namely, for every c > ηd, a complex drawn from Xd(n, c n ) is asymptotically almost surely not d-collapsible.
منابع مشابه
MATH690 - Topics in Random Topology - Literature
[1] Robert J. Adler, Omer Bobrowski, and Shmuel Weinberger. Crackle: The Homology of Noise. Discrete & Computational Geometry, 52(4):680–704, December 2014. [2] Noga Alon. On the edge-expansion of graphs. Combinatorics, Probability and Computing, 6(02):145–152, 1997. [3] Noga Alon and Joel H. Spencer. The probabilistic method. John Wiley & Sons, 2004. [4] Lior Aronshtam and Nathan Linial. The t...
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عنوان ژورنال:
- Random Struct. Algorithms
دوره 48 شماره
صفحات -
تاریخ انتشار 2016