Antisymmetric flows and strong oriented coloring of planar graphs Original Research Article

Nešetřil and Raspaud (Ann. Inst. Fourier 49 (3) (1999) 1037–1056) defined antisymmetric flow, which is a variant of nowhere zero flow, and a dual notion to strong oriented coloring. We give an upper bound on the number of colors needed for a strong oriented coloring of a planar graph, and hereby we find a small antisymmetric flow for any planar graph. In the proof we use a result from combinatorial number theory—the existence of large Sidon sets.