The critical-region equation for randomized graph coloring experiments

Let $G(n,k,p)$ be a random graph with $n$ vertices, $k$ partitions, and edge probability $p$ between vertices from distinct partitions. The critical region is the range of parameters in which the algorithm performs poorly.

Critical-region conjecture. The critical regions are characterized by the equation

$$\frac{2pn}{k} \approx \frac{16}{3}.$$

This conjecture was proposed on the basis of experimental results and concerns the narrow parameter interval where the algorithm's performance deteriorates. The supplied text gives no evidence that it has been proved or refuted.