Tight bound for k-connected orientations: is f(k) = 2k?

Determine whether every 2k-connected graph admits a k-connected orientation; that is, prove or refute that the minimum connectivity threshold f(k) for guaranteeing a k-connected orientation equals 2k.

Background

Nash-Williams showed that 2k-edge-connectivity suffices for k-arc-connected orientations. Thomassen conjectured an analogous vertex-connectivity threshold f(k). It is known that f(1)=2 and f(2)=4; the present paper proves f(k) ≤ 320k^2, but the exact threshold remains unknown.

The natural lower bound is 2k; whether this is tight is a longstanding problem in orientation theory.