Nowhere-zero flows on signed eulerian graphs

Abstract

This paper is devoted to a detailed study of nowhere-zero flows on signed eulerian graphs. We generalise 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 characterise 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~$A$.

17 pages, 1 figure

References in corpus (1)

• Flows on Bidirected Graphs

Cited by in corpus (2)

• Nowhere-zero flows on signed regular graphs
• Nowhere-zero flows in signed graphs: A survey