An 8-flow theorem for signed graphs
arxiv(2024)
摘要
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-color 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 Li et al. (European J. Combin. 108
(2023), 103627), which state that every flow-admissible signed
3-edge-colorable cubic graph admits a nowhere-zero 10-flow, and that every
flow-admissible signed hamiltonian graph admits a nowhere-zero 8-flow.
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