For every strictly 1-balanced graph F, the random graph G(n,p) gets an F-factor exactly at the sharp threshold where F-isolated vertices vanish, confirming Ruciński's conjecture.
Two moments suffice for Poisson ap- proximations: the Chen-Stein method.The Annals of Probability, pages 9–25, 1989
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Sharp Thresholds for Factors in Random Graphs
For every strictly 1-balanced graph F, the random graph G(n,p) gets an F-factor exactly at the sharp threshold where F-isolated vertices vanish, confirming Ruciński's conjecture.