Two-connected orientations of Eulerian graphs

A graph G = (V, E) is said to be weakly four-connected if G is 4-edge-connected and G – x is 2-edge-connected for every x ∈ V. We prove that every weakly four-connected Eulerian graph has a 2-connected Eulerian orientation. This verifies a special case of a conjecture of A. Frank . © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 230–242, 2006