# Orientation conjecture of Nash-Williams

Any $2k$-edge-connected (possibly infinite) multigraph admits a $k$-edge-connected orientation.
The conjecture is formulated by Nash-Williams who also proved the restriction of it to finite multigraphs; see Nash-Williams' strong orientation theorem. The first (and so far the only) breakthrough is due to C. Thomassen. He showed that a $8k$-edge-connected infinite multigraph admits a $k$-edge-connected orientation [1]. The conjecture is implied by its own restriction to countably infinite, locally finite multigraphs hence it is essentially a countable problem.