Zdeborová–Boettcher conjecture on max-cut and bisection width

Let $G$ be a random regular graph, and let the max-cut be a partition of its vertex set maximizing the number of crossing edges. Let the bisection width be the minimum number of crossing edges over all bisections of $G$. Zdeborová–Boettcher conjecture. In a random regular graph, the size of the max-cut is asymptotically equal to the number of edges minus the bisection width, asymptotically almost surely. This conjecture predicts a quantitative relation between the maximum cut and minimum bisection problems in random regular graphs. The supplied text gives no resolution status.