We consider the component structure of the random digraph D(n,p) inside the critical window $p = n^{-1} + \lambda n^{-4/3}$ . We show that the largest component $\mathcal{C}_1$ has size of order $n^{1/3}$ in this range. In particular we give explicit bounds on the tail probabilities of $|\mathcal{C}_1|n^{-1/3}$ .

Short duration cotton (Gossypium hirsutum L.) cultivar may be more profitable for the growers, as it will have shortened critical growth window for drought, heat and insect pests. Therefore, in the present research work, two cotton advance lines IUB-71 and IUB-73 along with an approved cotton cultivar IUB-13 were tested under four different sowing dates i.e. S1 (25th April), S2 (10th May), S3 (25th May) and S4 (10th June) in 2017 and 2018 under field condition. Field layout was RCBD factorial with four sowing dates as one factor and three cotton genotypes as another factor with three replications. Data were recorded for plant height, total number of nodes, bolls per plant, seed cotton yield (SCY), above ground fresh biomass (AGFB) and harvest index (HI). An overall decreasing trend with increasing sowing dates was observed in all the traits except HI that relatively increased in all the three genotypes. Within each sowing date, a higher value for each trait was observed for genotype IUB-73 except for AGFB might be due to higher reproductive allocation. It is concluded that IUB-73 due to superior SCY and HI specifically under late planting is best fit for short cotton seasons with reduced critical window for cotton management.

The largest components of the critical Erdős–Rényi graph, G(n, p) with p = 1 / n, have size of order n2/3 with high probability. We give detailed asymptotics for the probability that there is an unusually large component, i.e. of size an2/3 for large a. Our results, which extend the work of Pittel (2001), allow a to depend upon n and also hold for a range of values of p around 1 / n. We also provide asymptotics for the distribution of the size of the component containing a particular vertex.