Problem of the month July 2010

For July, the problem of the month remains the characterization of graphs having a k-connected orientation:

Is it true that a simple graph G has a k-connected orientation if and only if the deletion of any j<k nodes leaves a 2(k-j)-edge-connected graph?

The problem is open for k=2, and there are only a few partial results, see the problem page. The rooted version of the problem is also interesting; a candidate for the characterization is described on the discussion page of the problem.

The problem on the page Highly element-connected orientation has a similar flavor, although it probably requires different techniques.