The bipartition number $\tau (G)$ of a graph $G$ is the smallest number of pairwise edge disjoint complete bipartite graphs whose union is $G$. The independence number $\alpha (G)$ is the size of the largest independent subset of $G$.Is it true that, if $G$ is a random graph on $n$ vertices with edge probability $1/2$, then$$\tau (G)=n-\alpha (G)$$almost surely?