An 8-flow theorem for signed graphs

We prove that a signed graph admits a nowhere-zero 8-flow
provided that it is flow-admissible and the underlying graph
admits a nowhere-zero 4-flow. When combined with the 4-colour
theorem, this implies that every flow-admissible bridgeless
planar signed graph admits a nowhere-zero 8-flow. Our result
improves and generalizes previous results of L. Li, C. Li,
R. Luo, and C.-Q. Zhang (European J. Combin., 2023) which state
that every flow-admissible signed 3-edge-colourable cubic graph
admits a nowhere-zero 10-flow, and that every flow-admissible
signed hamiltonian graph admits a nowhere-zero 8-flow.

This is a joint work with R. Luo, E. Macajova, and C.-Q. Zhang.