Flows of 3-edge-colorable cubic signed graphs. (February 2023) - Li, Liangchen; Li, Chong; Luo, Rong; Zhang, Cun-Quan; Zhang, Hailiang
Abstract: Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction to cubic signed graphs. In this paper, we proved that every flow-admissible 3-edge-colorable cubic signed graph admits a nowhere-zero 10-flow. This together with the 4-color theorem implies that every flow-admissible bridgeless planar signed graph admits a nowhere-zero 10-flow. As a byproduct, we also show that every flow-admissible hamiltonian signed graph admits a nowhere-zero 8-flow.