Frieze–Krivelevich–Michaeli conjecture on d-connectivity under restricted budget

Let $d$ be a positive integer and let $\varepsilon>0$. A $(t,b)$-strategy of Builder is a strategy in the random edge-ordering process that makes decisions during the first $t$ proposed edges while accepting at most $b$ edges. A graph is $d$-connected if deleting fewer than $d$ vertices leaves it connected.

Frieze–Krivelevich–Michaeli conjecture. If

$$t\ge (1+\varepsilon) n\log n/2$$

and

$$b\ge (1+\varepsilon)dn/2,$$

then there exists a $(t,b)$-strategy of Builder such that $G_t$ is a.a.s. $d$-connected.

This conjecture concerns the threshold for achieving $d$-connectivity when Builder has both a waiting-time limit and a budget on the number of accepted edges. The source recalls it from Frieze, Krivelevich and Michaeli; its resolution is not specified here.