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In this short note, we consider a graph process recently introduced byFrieze, Krivelevich and Michaeli. In their model, the edges of the completegraph $K_n$ are ordered uniformly at random and are then revealed consecutivelyto a player called Builder. At every round, Builder must decide if they acceptthe edge proposed at this round or not. We prove that, for every $d\ge 2$,Builder can construct a spanning $d$-connected graph after $(1+o(1))n\log n/2$rounds by accepting $(1+o(1))dn/2$ edges with probability converging to 1 as$n\to \infty$. This settles a conjecture of Frieze, Krivelevich and Michaeli.

$d$-connectivity of the random graph with restricted budget