Nowhere-zero 5-flow on signed ladders

Abstract

In 1983, Bouchet conjectured that every flow-admissible signed graph admits a nowhere-zero $6$-flow. In this paper, we prove that Bouchet's conjecture holds for all signed ladders, circular and M\"obius ladders. In fact, all signed ladders, circular and M\"obius ladders admit a nowhere-zero $5$-flow except for one case of signed circular ladders. Of course, the exception also has a nowhere-zero $6$-flow.