On Erdős-Ko-Rado for random hypergraphs II

2014/06/23 by Arran Hamm, Jeff Kahn, Hamm, Arran +1
Computer Science · Mathematics · #05C65 #05D05 #05D40 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1406.5793

openalex publication_date 2014/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by 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→ ∞), H_k (n,p) has the "Erdős-Ko-Rado property." We also mention a similar random version of Sperner's Theorem.

Citations

• On a Problem of Formal Logic

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