Cycle Lengths and Graph Orientations
Oliver Pretzel, Dale Youngs · SIAM Journal on Discrete Mathematics · 1990
Those functions defined on the cycles of a finite graph G that can be the flow difference of an orientation of G are characterized. The result is applied to give a proof of Bandelt’s Theorem stating that all (Hasse-) diagram orientations of a planar graph G have zero flow difference on all cycles if and only if G has a cycle basis of 4-cycles.