# Random triangles in random graphs

@article{Heckel2018RandomTI,
title={Random triangles in random graphs},
author={Annika Heckel},
journal={arXiv: Combinatorics},
year={2018}
}
• A. Heckel
• Published 23 February 2018
• Mathematics
• arXiv: Combinatorics
In a recent paper, Oliver Riordan shows that for $r \ge 4$ and $p$ up to and slightly larger than the threshold for a $K_r$-factor, the hypergraph formed by the copies of $K_r$ in $G(n,p)$ contains a copy of the binomial random hypergraph $H=H_r(n,\pi)$ with $\pi \sim p^{r \choose 2}$. For $r=3$, he gives a slightly weaker result where the density in the random hypergraph is reduced by a constant factor. Recently, Jeff Kahn announced an asymptotically sharp bound for the threshold in Shamir's… Expand
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Random cliques in random graphs
We show that for each $r\ge 4$, in a density range extending up to, and slightly beyond, the threshold for a $K_r$-factor, the copies of $K_r$ in the random graph $G(n,p)$ are randomly distributed,Expand
Factors in random graphs
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