In a recent paper, Oliver Riordan shows that for and p up to slightly larger than the threshold Kr-factor, hypergraph formed by copies of Kr in G(n, p) contains copy binomial random with . For r = 3, he gives weaker result where density is reduced constant factor. Recently, Jeff Kahn announced an asymptotically sharp bound Shamir's matching problem all With Riordan's result, this immediately im...