NOWHERE-ZERO FLOWS ON SIGNED EULERIAN GRAPHS.

This paper is devoted to a detailed study of nowhere-zero flows on signed Eulerian graphs. We generalize the well-known fact about the existence of nowhere-zero 2-flows in Eulerian graphs by proving that every signed Eulerian graph that admits an integer nowhere-zero flow has a nowhere-zero 4-flow. We also characterize signed Eulerian graphs with flow number 2, 3, and 4, as well as those that do not have an integer nowhere-zero flow. Finally, we discuss the existence of nowhere-zero A-flows on signed Eulerian graphs for an arbitrary Abelian group A. [ABSTRACT FROM AUTHOR]