Two-connected orientations of Eulerian graphs

Authors:
Alex R. Berg;Tibor Jordán
Affiliations:
BRICS (Basic Research in Computer Science, Centre of the Danish National Research Foundation), University Of Aarhus, Aabogade 34 8200 Aarhus N, Denmark;Department of Operations Research, Eötvös University, Pázmány Péter Sétány 1-C, 1117 Budapest, Hungary
Venue:
Journal of Graph Theory
Year:
2006

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Abstract

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