Rainbow-connectivity game threshold conjecture

For the rainbow-connectivity game $\mathcal{C}_{s,n}$, let $b_{\mathcal{C}_{s,n}}$ denote its threshold bias. Assume that $s=\omega(\log(n))$. Rainbow-connectivity threshold conjecture.

$$b_{\mathcal{C}_{s,n}}=(1+o(1))\frac{sn}{\log(n)}.$$

The paper determines the threshold up to a multiplicative factor $2$ in this regime, while the displayed asymptotic equality remains conjectural.