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On Erdős–Ko–Rado for Random Hypergraphs II

Part of: Graph theory Extremal combinatorics

Published online by Cambridge University Press:  18 October 2018

A. HAMM  and
J. KAHN
A. HAMM
Affiliation:
Department of Mathematics, Winthrop University, Rock Hill, SC 29733, USA (e-mail: [email protected])
J. KAHN
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA (e-mail: [email protected])
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Abstract

Denote by ${\mathcal H}_k$(n, p) the random k-graph in which each k-subset of {1,. . .,n} is present with probability p, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed ε > 0 such that if n = 2k + 1 and p > 1 - ε, then w.h.p. (that is, with probability tending to 1 as k → ∞), ${\mathcal H}_k$(n, p) has the ‘Erdős–Ko–Rado property’. We also mention a similar random version of Sperner's theorem.

MSC classification

Primary: 05D40: Probabilistic methods
Secondary: 05D05: Extremal set theory 05C65: Hypergraphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Issue 1 , January 2019 , pp. 61 - 80
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

Supported by NSF grant DMS1201337.

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